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This study deals with exact solutions and soliton dynamics of Burgers equation. The Lie symmetry method under one parameter transformation is employed to establish symmetry condition, infinitesimals and their commutative relations. In consequence, the similarity variables are derived and cause to first symmetry reduction. A twice employment of method allows further symmetry reductions of test equations and results to systems of ODEs. Then, the ODEs have been integrated under parametric constraints and evolve desired exact solutions. These solutions consist of all the functions f 1 (t) , f 2 (t) , g 1 (y) , g 2 (y) existed in infinitesimals, more arbitrary functions F(X), H(X) and several arbitrary constants that make obtained results generalize than previous findings. To analyze the nature of physical phenomena associated with Burgers equation, these solutions have been supplemented with numerical simulation. Consequently, single soliton, doubly soliton, multisoliton, asymptotic nature, soliton fusion and fission nature are discussed systematically. Moreover, the Lagrangian formulation and conserved vectors associated with Lie symmetries are obtained. [ABSTRACT FROM AUTHOR]

We propose a modification to the nonlinear term of the three-dimensional incompressible Navier–Stokes equations (NSE) in either advective or rotational form which “calms” the system in the sense that the algebraic degree of the nonlinearity is effectively reduced. This system, the calmed Navier–Stokes Equations (calmed NSE), utilizes a “calming function” in the nonlinear term to locally constrain large advective velocities. Notably, this approach avoids the direct smoothing or filtering of derivatives, thus we make no modifications to the boundary conditions. Under suitable conditions on the calming function, we are able to prove global well-posedness of calmed NSE and show the convergence of calmed NSE solutions to NSE solutions on the time interval of existence for the latter. In addition, we prove that the dynamical system generated by the calmed NSE in the rotational form possesses both an energy identity and a global attractor. Moreover, we show that strong solutions to the calmed equations converge to strong solutions of the NSE without assuming their existence, providing a new proof of the existence of strong solutions to the 3D Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

Copyright of Afyon Kocatepe University Journal of Science & Engineering / Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi is the property of Afyon Kocatepe University, Faculty of Science & Literature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this article, we briefly review the random choice method (RCM) and ADER methods for solving one and two-dimensional hyperbolic conservation laws. The main advantage of RCM is that it computes discontinuities with infinite resolution. In this method, the original problem is reduced to a set of local Riemann problems (RPs). The exact solutions of these RPs are used to form the solution of the original problem. However, RCM has the following disadvantages: (1) one should solve the RP exactly, however, the exact solutions are usually complex and unavailable for many problems. (2) The accuracy of the smooth region of the flow is poor. ADER methods are explicit, one-step schemes with a very high order of accuracy in time and space. They depend on the solution of the generalized RP (GRP) exactly. In Zahran (J Math Anal Appl 346:120–140, 2008), an improved version of ADER methods (central ADER) was introduced where the RPs were solved numerically and used central fluxes, instead of upwind fluxes. The improved central ADER schemes are more accurate, faster, simple to implement, RP solver free, and need less computer memory. To fade the drawbacks of the above schemes and keep their advantages, we propose, in this paper, an improved version of the RCM. We merge the central ADER technique with the RCM. The resulting scheme is called Central RCM (CRCM). The improvements are listed as follows: we use the WENO reconstruction for the initial data instead of constant reconstruction in RCM, we solve the RPs numerically by using central finite difference schemes and use random sampling to update the solution, as the original RCM. Here we use the staggered and non-staggered RCM. To enhance the accuracy of the new methods, we use a third-order TVD flux (Zahran in Bull Belg Math Soc Simon Stevin 14:259–275, 2007), instead of a first-order flux. Compared with the original RCM and the central ADER, the new methods combine the advantages of RCM, ADER, and central finite difference methods as follows: more accurate, very simple to implement, need less computer memory, and RP solver free. Moreover, the new methods capture the discontinuities with infinite resolution and improve the accuracy of the smooth parts. The new methods have less CPU time than the central ADER methods, this is due to less flux evaluation in CRCM. An extension of the schemes to general systems of nonlinear hyperbolic conservation laws in one and two dimensions is presented. We present several numerical examples for one and two-dimensional problems. The results confirm that the presented schemes are superior to the original RCM, ADER, and central ADER schemes. [ABSTRACT FROM AUTHOR]

In this short note, we prove that given initial data u 0 ∈ H s (R) with s > 3 2 and for some T > 0 , the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in L ∞ (0 , T ; H s (R)) to the inviscid Burgers equation as the filter parameter α tends to zero. This is a complement of our recent result on the zero-filter limit. [ABSTRACT FROM AUTHOR]

In this paper, we focus on zero-filter limit problem for the Camassa-Holm equation in the more general Besov spaces. We prove that the solution of the Camassa-Holm equation converges strongly in L ∞ (0 , T ; B 2 , r s (R)) to the inviscid Burgers equation as the filter parameter α tends to zero with the given initial data u 0 ∈ B 2 , r s (R) . Moreover, we also show that the zero-filter limit for the Camassa-Holm equation does not converges uniformly with respect to the initial data in B 2 , r s (R) . [ABSTRACT FROM AUTHOR]

In this paper, we study the solvability of one initial-boundary value problem for the Burgers equation with periodic boundary conditions in a nonlinearly degenerating domain. In this paper, we found an orthonormal basis for domains with time-varying boundaries. On this basis, we use the Faedo–Galerkin method to prove theorems about the unique solvability of the problem under consideration. We also present some numerical results in the form of graphs of solutions to the problem under study for various initial data. [ABSTRACT FROM AUTHOR]

We consider a periodic problem for a singularly perturbed parabolic reaction–diffusion–advection equation of the Burgers type with the modulus advection; it has a solution in the form of a moving front. We formulate conditions for the existence of such a solution and construct its asymptotic approximation. We pose a control problem where the required front propagation law is implemented by a specially chosen boundary condition. We construct an asymptotic solution of the boundary control problem. Using the asymptotic method of differential inequalities, we estimate the accuracy of the solution of the control problem. We propose an original numerical algorithm for solving singularly perturbed problems involving the modulus advection. [ABSTRACT FROM AUTHOR]

To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic iteration or Picard–Lindelöf iteration), where at each iteration a linear inhomogeneous system of differential equations has to be solved. This is done by the exponential block Krylov subspace (EBK) method. Thus, we have an inner-outer iterative method, where iterative approximations are determined over a certain time interval, with no time stepping involved. This approach has recently been shown to be efficient as a time-parallel integrator within the PARAEXP framework. In this paper, convergence behavior of this method is assessed theoretically and practically. We examine efficiency of the method by testing it on nonlinear Burgers, Liouville–Bratu–Gelfand, and nonlinear heat conduction equations and comparing its performance with that of conventional time-stepping integrators. [ABSTRACT FROM AUTHOR]

We present some results concerning the control of the Burgers equation. We analyze a bi-objective optimal control problem and then the hierarchical null controllability through a Stackelberg–Nash strategy, with one leader and two followers. The results may be viewed as an extension to this nonlinear setting of a previous analysis performed for linear and semilinear heat equations. They can also be regarded as a first step in the solution of control problems of this kind for the Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

In this work, the (2+1)-dimensional Painlevé integrable Burgers equation is investigated. By applying a certain unified method, some analytical solutions, involving rational functions, trigonometric functions and hyperbolic functions, are achieved. In order to predict the wave dynamics, several three-dimensional and two-dimensional graphs and contour profiles are constructed. Bright, dark, periodic, kink, anti-kink, singular, singular periodic, bell-shaped waves are thus obtained. The dynamics of these solutions can be illustrated graphically by choosing appropriate values for the parameters involved. Due to the presence of arbitrary constants in these derived solutions, they can be used to explain a variety of qualitative traits present in wave phenomena. The approach is efficient to algebraic computation and it can be used to categorize a wide range of wave forms, as shown by the demonstrated soliton solutions. Travelling wave solutions are converted into solitary wave solutions when certain values are set for the parameters. Using the Wolfram program Mathematica, we sketch the figures for various values of the associated parameters in order to closely examine the obtained solitons. [ABSTRACT FROM AUTHOR]

This article utilizes the Aboodh residual power series and Aboodh transform iteration methods to address fractional nonlinear systems. Based on these techniques, a system is introduced to achieve approximate solutions of fractional nonlinear Korteweg-de Vries (KdV) equations and coupled Burger's equations with initial conditions, which are developed by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. As a result, the Aboodh residual power series and Aboodh transform iteration methods for integer-order partial differential equations may be easily used to generate explicit and numerical solutions to fractional partial differential equations. The results are determined as convergent series with easily computable components. The results of applying this process to the analyzed examples demonstrate that the new technique is very accurate and efficient. [ABSTRACT FROM AUTHOR]

In this article, non-standard compact finite difference schemes are constructed for the numerical approximation to first- and second-order derivatives. The proposed compact schemes have eighth order of accuracy and are tri-diagonal in nature, making use of a stencil smaller than those of conventional tri-diagonal compact finite difference schemes of the same order. They also possess high resolution properties and more resolving efficiency than conventional schemes. Some numerical experiments have been carried out, showing the good performance of the proposed schemes. Furthermore, the proposed schemes have been applied to solve with great efficiency the well-known Burgers equation. [ABSTRACT FROM AUTHOR]

A qualitative analysis of the electron-acoustic wave is taken in a collisional plasma having two-temperature electrons with a fixed ion background, where hot electrons follow kappa distribution. The collision between stationary ions and cold electrons is considered. Using reduced perturbation technique, the Burgers equation for the plasma system is derived. Using traveling wave transformation, we obtain the dynamical system corresponding to the plasma system. Phase plane analysis is used in the dynamical system to study different kinds of wave features for the considered plasma system. Moreover periodic wave features and shock wave features are investigated in accordance to periodic orbits and heteroclinic orbits obtained in the phase portrait. Role of the superthermal parameter (κ ), speed of the travelling wave (U) and α = n c 0 / n h 0 (where n c 0 denotes the number density of cold electrons in equilibrium and n h 0 denotes the number density of hot electrons in equilibrium) are shown on the electron-acoustic periodic waves and shock waves structures. The results hold relevance and significance in the context of space plasma. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cauchy problem for the Burgers equation in the line. We shall prove that this problem is ill-posed in the Sobolev space H s (R) with 1 ≤ s < 3 2 in the sense of "norm inflation" by constructing an explicit example of initial data. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive support domain scheme is proposed to the in-compressible fluid flow based on the localized radial basis function collocation method (LRBFCM). The idea of the adaptive support domain avoids complex mathematical derivations of the finite difference method (FDM). Unlike other upwind schemes in the LRBFCM, the support domain uses the sampling nodes similar to different finite difference schemes, and the improved LRBFCM is further applied to the in-compressible fluid flows. Considering the Kronecker tensor product and Cholesky decomposition techniques, the improved LRBFCM can be easily used to the lid-driven problems with Reynolds numbers up to 100,000 by a simple mathematical derivation. The proposed LRBFCM has an adaptive support domain similar to the finite difference schemes with much less CPU time costs. [ABSTRACT FROM AUTHOR]

In this paper, the periodic solutions of the Burgers equation are expanded in a power series with respect to the viscosity coefficient ε which gives a recurrence relation among the approximate functions. Then, the general form of the Fourier expansions for the approximate functions are given by induction, and it is proved that the Fourier series of each approximate function is uniformly and absolutely convergent. [ABSTRACT FROM AUTHOR]

One-dimensional flows of an incompressible viscoelastic polymer fluid that are qualitatively similar to the solutions of Burgers' equation are described on the basis of mesoscopic approach for the first time. The corresponding initial boundary-value problem is posed for the system of quasilinear differential equations. The numerical algorithm for solving it is designed and verified. The algorithm uses the explicit fifth-order scheme to approximate unknown functions with respect to time variable and the rational barycentric interpolations with respect to space variable. A method for localization of singular points of the solution in the complex plain and for adaptation of the spatial grid to them is implemented using the Chebyshev-Padé approximations. Two regimes of evolution of the solution to the problem are discovered and characterized while using the algorithm: regime 1—a smooth solution exists in a sufficiently large time interval (the singular point moves parallel to the real axis in the complex plane); regime 2—the smooth solution blows up at the beginning of evolution (the singular point reaches the segment of the real axis where the problem is posed). We study the influence of the rheological parameters of fluid on the realizability of these regimes and on the length of time interval where the smooth solution exists. The obtained results are important for the analysis of laminar-turbulent transitions in viscoelastic polymer continua. [ABSTRACT FROM AUTHOR]

We investigate the system of non-stationary one-dimensional equations consisting of a parabolic Burgers equation for the velocity of a viscous gas and a hyperbolic Hopf equation for the velocity of solid particles. The Burgers and Hopf equations are connected into a system due to relaxation terms simulating the momentum transfer between the carrier phase (gas) and the dispersed phase (particles). The momentum transfer intensity is inversely proportional to the relaxation time of the particle velocity to the gas velocity (stopping time). A dispersion relation is constructed for this system. A particular solution corresponding to the damping of a low-amplitude sound wave is found. For an infinitely short velocity relaxation time, the effective viscosity of the gas-dust medium is derived, which is determined by the viscosity of the gas and the mass fraction of particles in the mixture. The Lie algebra of symmetries of Burgers–Hopf system is found. Invariant submodels with respect to the basis operators of the symmetry algebra are derived. These submodels are explicitly integrated, except for one that defines stationary motion. For this submodel, a code has been developed for the numerical generation of particular solutions of the system. It is shown that the invariant solution determined by this submodel, in the asymptotic case of infinitely short velocity relaxation time also makes it possible to obtain the effective viscosity of the gas-dust mixture. Moreover, this effective viscosity coincides with the viscosity value determined from the dispersion relation. [ABSTRACT FROM AUTHOR]

This article utilizes the Aboodh residual power series and Aboodh transform iteration methods to address fractional nonlinear systems. Based on these techniques, a system is introduced to achieve approximate solutions of fractional nonlinear Korteweg-de Vries (KdV) equations and coupled Burger’s equations with initial conditions, which are developed by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. As a result, the Aboodh residual power series and Aboodh transform iteration methods for integer-order partial differential equations may be easily used to generate explicit and numerical solutions to fractional partial differential equations. The results are determined as convergent series with easily computable components. The results of applying this process to the analyzed examples demonstrate that the new technique is very accurate and efficient.

Firstly, this study uses a partial differential equation to conduct experimental research on the teaching effect of music education. Secondly, the convolutional neural network method is used to optimize the weighted factors in the traditional finite volume method. This makes the calculation results of the model more accurate under the condition of coarse particles. It is found that the model can solve Burgers and level set equations accurately and effectively. This method can evaluate the teaching effect of music education more accurately and improve students’ learning products of music.

We establish a space-time integral estimate of the difference of solutions of non-degenerate scalar conservation laws. It is valid over the maximal domain (0 , T max ) × ℝ d in which the solutions are shock-free, and it fails beyond T max . When comparing a solution with its shifts, we deduce a Besov-like estimate at the development of its first singularity. [ABSTRACT FROM AUTHOR]

We study two types of one-dimensional stochastic Burgers equations: Burgers equations with stochastic fluxes and Burgers equations perturbed by transport noise. Using the methods of stochastic characteristics and the characteristics perturbed by noise, respectively, we obtain the probabilities for the occurrence of shocks before and after a given time. Compared with the deterministic equations, in case of small initial data the occurrence time of shocks for Burgers equations with stochastic fluxes will be delayed with large probability, but this conclusion is only true for Burgers equations perturbed by the transport noise with large initial data. [ABSTRACT FROM AUTHOR]

We present the numerical application of a meshfree algorithm for the solution of fully nonlinear PDEs by Monte Carlo simulation using branching diffusion trees coded by the nonlinearities appearing in the equation. This algorithm is applied to the numerical solution of modified and non-Newtonian Burgers equations, and to a problem with boundary conditions in fluid dynamics, by the computation of a Poiseuille flow. Our implementation uses neural networks that yield a functional space-time domain estimation, and includes numerical comparisons with the deep Galerkin (DGM) and deep backward stochastic differential equation (BSDE) methods. [ABSTRACT FROM AUTHOR]

A multiple‐relaxation‐time (MRT) lattice Boltzmann (LB) model is developed to solve Burgers equation. The general MRT‐LB model can be thought as a three‐level nonlinear finite difference scheme. Maximum value principle has been proved, and the existence, uniqueness, and stability parameters are discussed for the three‐level finite difference scheme of MRT‐LB model. Numerical stability analysis shows that the MRT‐LB model is not only a three‐level nonlinear finite difference one but also has the good numerical stability. Numerical solutions have been compared with the exact solutions and other LB models reported in previous studies. The experiments results show that the scheme is accurate and effective for Burgers equation. [ABSTRACT FROM AUTHOR]

In this paper we study a solution existence problem for the singular nonlinear Burgers equation where and , with small parameter ε under the boundary conditions and the oscillating initial condition The first derivative of the operator F at the solution point is assumed to be degenerate, i.e., is not surjective. The existence of a continuous solution to this nonlinear problem is proved by applying p-regularity theory and the Michael selection theorem. [ABSTRACT FROM AUTHOR]

This paper is dedicated to finding the traveling wave solutions of the loaded Burgers equation. We show how to find the solutions via the (G′/G) - expansion method which is one of the most effective ways of finding solutions. When the parameters are taken as special values, the solitary waves are also derived from the traveling waves. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. This method is easy to implement using well-known software packages, which allows you to solve complex nonlinear evolution equations of mathematical physics. [ABSTRACT FROM AUTHOR]

Nonlinear acoustics is a critical area of study with practical applications in fields such as underwater communications, medical imaging, non-destructive testing, and sonar. This paper offers a comprehensive analysis of the Westervelt and Burgers equations, along with their related boundary problems, and investigates the characteristics of parametric generation, thereby making substantial advancements in the theoretical comprehension of nonlinear acoustic waves. Our analysis sheds new light on the dynamics of nonlinear acoustic waves and their behavior in various media, providing valuable insights into the physics of sound propagation. Finally, parametric effects can be intelligently exploited for communication applications. Thus, through the appropriate selection of encodings, it is possible to develop underwater acoustic communication systems with greater directivity and range than classical systems.

In this manuscript, the Korteweg-de Vries-Burgers (KdV-Burgers) partial differential equation (PDE) is investigated under nonlocal operators with the Mittag-Leffler kernel and the exponential decay kernel. For both fractional operators, the existence of the solution of the KdV-Burgers PDE is demonstrated through fixed point theorems of α-type ϝ contraction. The modified double Laplace transform is utilized to compute a series solution that leads to the exact values when fractional order equals unity. The effectiveness and reliability of the suggested approach are verified and confirmed by comparing the series outcomes to the exact values. Moreover, the series solution is demonstrated through graphs for a few fractional orders. Lastly, a comparison between the results of the two fractional operators is studied through numerical data and diagrams. The results show how consistently accurate the method is and how broadly applicable it is to fractional nonlinear evolution equations.

The purpose of this article is to derive a class of multi-soliton solutions of the Burgers equation employing Darboux transformation with the help of the Lax pair. By means of an effective transformation, the Burgers equation is reduced to a suitable form, and accordingly, the Lax pair of the said equation is derived utilising the Ablowitz–Kaup–Newell–Segur (AKNS) approach. Thus, the integrability of the Burgers equation is confirmed. To find an effective solution for the Burgers equation, for the first time, we apply the Darboux transformation through the Lax pair and explore new types of one-soliton solutions and two-soliton solutions of the Burgers equation. These solutions provide some new features of the Burgers equation. To the best of our knowledge, this is the first study in which a parabolic type of structure is found in the Burgers system. Moreover, taking these solutions as the seed solution, higher-order multi-soliton solution can also be generated. Finally, some important three-dimensional plots of the wave solutions are presented to visualise the dynamics of the model. [ABSTRACT FROM AUTHOR]

In this work, we design, analyze, and test the multiwavelets Galerkin method to solve the two‐dimensional Burgers equation. Using Crank–Nicolson scheme, time is discretized and a PDE is obtained for each time step. We use the multiwavelets Galerkin method for solving these PDEs. Multiwavelets Galerkin method reduces these PDEs to sparse systems of algebraic equations. The cost of this method is proportional to the number of nonzero coefficients at each time step. The results illustrate, by selecting the appropriate threshold while the number of nonzero coefficients reduces, the error will not be less than a certain amount. The L2 stability and convergence of the scheme have been investigated by the energy method. Illustrative examples are provided to verify the efficiency and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

A multi-domain Galerkin method is presented for the Burgers equation, whose solutions behave differently at positive infinity and negative infinity. The original problem is transformed into a problem with general variable coefficients and homogeneous boundary conditions at infinities by using the auxiliary function, which is capable of being reformulated as a suitable variational formulation that is the most convenient for analysing numerical error. As an application, the composite spectral scheme with numerical integration is provided for the underlying problem on the whole line, which is easy to deal with problems concerning general variable coefficients. Some composite generalized Laguerre–Legendre interpolations on the whole line are established. The convergence and stability of the proposed algorithm are proved. Numerical results show the efficiency of this approach and agree well with the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this work, we study the existence, uniqueness and regularity of the solution to a semilinear Cauchy–Dirichlet problem with variable coefficients, using the Faedo–Galerkin method. We applied this study to a nonhomogeneous Burgers problem considered in a nonparabolic domain. We give a new regularity result of the solution in an anisotropic Sobolev space. [ABSTRACT FROM AUTHOR]

The conditions for the outflow of an underexpanded supersonic jet from an experiment conducted at the Laboratory for Turbulent Research in Aerospace and Combustion (LTRAC), Monash University, Australia are considered. The characteristic parameters of linear and nonlinear transport for the LTRAC jet are analyzed using LES solutions from the near and far acoustic fields. In both cases, the fulfillment of the conditions of the linear scenario of sound transfer over distances characteristic of the LTRAC acoustic experiment is shown. To verify the theoretical estimates, numerical solutions of the spherical Burgers equation are also obtained using the initial data from the LES calculation. Solutions are obtained without and in the presence of a term in the Burgers equation corresponding to quadratic nonlinearity. The solutions respond to sound transfer at distances that are orders of magnitude greater than the distance between the acoustic microphone and the jet in the LTRAC experiment. [ABSTRACT FROM AUTHOR]

In this paper, we study the small-time global null controllability of the generalized Burgers' equations yt + γ|y|γ-1yx — yxx = u(t) on the segment [0, 1]. The scalar control u(t) is uniform in space and plays a role similar to the pressure in higher dimension. We set a right Dirichlet boundary condition y(t, 1) = 0, and allow a left boundary control y(t, 0) = v(t). Under the assumption γ > 3/2 we prove that the system is small-time globally null controllable. Our proof relies on the return method and a careful analysis of the shape and dissipation of a boundary layer. [ABSTRACT FROM AUTHOR]

Theoretical investigation of dust acoustic shock waves (DAShWs) in an unmagnetized collisionless multicomponent dusty plasma of the Jupiter's atmosphere featuring kappa distributed ions, electrons, solar wind electrons and their interaction with the positive dust particles and the streaming protons originating from the solar wind was made. In the framework of reductive perturbation method, the KdV–Burgers equation has been derived to explain the dynamics of the dust acoustic shock waves. The evolution of the oscillatory shock waves also was illustrated. The effects of various physical parameters namely, the temperature ratio, fluid viscosity, superthermality and density of charged particles were analyses. The combined impact of these parameters greatly influence the characteristics of the shock waves. The present investigation may be useful to understand the underlying properties of various types of nonlinear structures and to explore the existence of dust acoustic shock waves in the Jupiter's atmosphere. [ABSTRACT FROM AUTHOR]

A dusty plasma consisting of ions following the Cairns–Tsallis (C–T) distribution, Boltzmann electrons, and negatively charged dust as a fluid is considered in the presence of a polarization force to investigate higher order dust acoustic (DA) nonlinear structures. Using the reductive perturbation technique, the Burgers and higher order Burgers equations are derived and the Tanh method is applied to determine the solutions of the Burgers equations. Based on the solutions to these nonlinear equations, the influence of various parameters on the features of the dust acoustic shocks and dressed shocks has been studied. The dynamics of DA shocks with the contribution of higher order corrections has been analysed to see the formation of dressed shocks. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mathematics, Mechanics & Computer Science is the property of Al-Farabi Kazakh National University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)