Search

Abstract: For Adlerʼs equation in the Viallet form and Yamilovʼs discretisation of the Krichever–Novikov equation we present new recursion and Hamiltonian operators. This new recursion operator and the recursion operator found in [A.V. Mikhailov, et al., Theor. Math. Phys. 167 (2011) 421, arXiv:1004.5346] satisfy the spectral curve associated with the equation. [Copyright &y& Elsevier]

Abstract: Time evolution of two interacting qubits under the influence of thermal reservoirs is considered. When there is only one excitation in the whole system, an exact reduced dynamics can be obtained. The result is compared with those obtained by the time-convolutionless and time-convolution quantum master equations in the second order approximation. [ABSTRACT FROM AUTHOR]

Abstract: The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka–Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Bäcklund transformation between these integrable systems. [ABSTRACT FROM AUTHOR]

Abstract: In this Letter, we consider the general expressions of peaked traveling wave solutions for CH and CH-γ equations. The orbital stability of these peakons are directly proved in the norm. Some previous results are extended. [Copyright &y& Elsevier]

Abstract: A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is developed to construct the exact solutions for a generalized Camassa–Holm equation and a nonlinear dispersive equation with variable coefficients. It is shown that the variable coefficients of the derivative terms in the equations cause the qualitative change in the physical structures of the solutions. [Copyright &y& Elsevier]

Abstract: In this Letter we use the Exp-function method for analytic treatment for the modified Benjamin–Bona–Mahony equations. New solitonary solutions are formally derived. The change of the parameters, that will drastically change the characteristics of the equations, is examined. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving high-dimensional nonlinear evolutions in mathematical physics. [Copyright &y& Elsevier]

Abstract: Exact solutions, including the periodic travelling and non-travelling wave solutions, are presented for the nonlinear Klein–Gordon equation with imaginary mass. Some arbitrary functions are permitted in the periodic non-travelling wave solutions, which contribute to various high dimensional nonlinear structures. [Copyright &y& Elsevier]

Abstract: In this Letter, a generalized auxiliary equation method is used to construct exact solutions of the ()-dimensional breaking soliton equations. As a result, many new and more general exact non-traveling wave and coefficient function solutions are obtained including soliton-like solutions, trigonometric function solutions, exponential solutions and rational solutions, each of which contains an arbitrary function of two variables. It is shown that the generalized auxiliary equation method provides a powerful mathematical tool for solving many nonlinear partial differential equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: In this Letter, the Exp-function method is used to obtain generalized solitonary solutions and periodic solutions of a KdV equation with variable coefficients. It is shown that the Exp-function method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations with variable coefficients in mathematical physics. [Copyright &y& Elsevier]

Abstract: The generalized Jacobi elliptic function expansion method is used with a computerized symbolic computation for constructing the new exact traveling wave solutions. The validity and reliability of the method is tested by its applications on a class of nonlinear evolution equations of special interest in mathematical physics. As a result, many exact traveling wave solutions are obtained which include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: The extended mapping method with a computerized symbolic computation is used to drive some new exact solutions of four nonlinear evolution equations in mathematical physics. As a result, many exact travelling wave solutions are obtained which include new solitary wave solutions, triangular and hyperbolic functions. Solutions in the limiting cases have also been studied. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: By means of computerized symbolic computation and a modified extended tanh-function method for constructing multiple traveling wave solutions of nonlinear physical equations is presented and implemented in a computer algebraic system. Applying this method, we consider some of nonlinear equations of special interest in physics namely, the Broer–Kaup–Kupershmidt, nonlinear coupled plasma, and coupled-nonlinear reaction–diffusion equations. As a results, we can successfully recover the previously known solitary wave solutions that had been found by other sophisticated methods. The method is straightforward and concise, and it can also be applied to other nonlinear equations in physics. [Copyright &y& Elsevier]

Abstract: A method to obtain the Schlesinger transformations for the standard discrete second Painlevé equation, d–PII, is given. The procedure involves formulating a Riemann–Hilbert problem for a transformation matrix which transforms the solution of the linear problem but leaves the associated monodromy data the same. [Copyright &y& Elsevier]

Abstract: We investigate stability of localized time-periodic states (pulsons) of a real scalar field satisfying the Klein–Gordon equation with the logarithmic nonlinearity. It is shown that the pulsons of any amplitudes, remaining well-localized objects, lose their coherence with time. We thus conclude that, strictly speaking, all pulsons of the model considered are unstable. Nevertheless, for some amplitudes the rate of the coherence breaking is found to be very small, so that the corresponding pulsons are long-lived. [Copyright &y& Elsevier]

Abstract: The motion of a magnetized heavy top hovering in a magnetic field is analyzed by discretization of the Chetayev equation for the heavy magnetic top. The resulting dynamical system is integrated numerically using different integrators based on the splitting of the Hamiltonian and on the discrete gradient concept. The numerical preservation properties of the first integrals and the adiabatic invariant for the magnetic top are also discussed. [Copyright &y& Elsevier]