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In this work, we study the asymptotic characteristics of high‐order solitons for the focusing Kundu–Eckhaus (KE) equation. Based on the loop group theory, we construct the general Darboux transformation within the framework of Riemann–Hilbert problems to derive the general high‐order soliton solution. Using high‐order Bäcklund transformation, we derive the leading order term of the determinant solution to obtain the asymptotic representation for the high‐order soliton solution. Furthermore, this method is also extended to the construction of more general high‐order cases with multiple poles. We further find that if a soliton propagates along the logarithm characteristic curve, the high‐order soliton can be decomposed into n$$ n $$ individual solitons with the same amplitude and velocity. Finally, these solutions are theoretically and graphically analyzed in detail. [ABSTRACT FROM AUTHOR]

Two new monoterpenoid indole alkaloids, named taberibogines E and F (1 and 2), together with three known ones (3–5) were isolated from the stems of Tabernaemontana bovina Lour (Apocynaceae). Their structures including absolute configurations were elucidated from a combination of NMR and HRESIMS data and NMR calculations as well as DP4+ probability analyses. Compounds 1 and 2 exhibited inhibitory effects on LPS-induced nitric oxide (NO) production in RAW 264.7 macrophages. [ABSTRACT FROM AUTHOR]

In this study, we present the rigorous theory of the robust inverse scattering method for the discrete high-order nonlinear Schrödinger (HNLS) equation with a nonzero boundary condition (NZBC). Using the direct scattering problem, we deduce the analyticity, symmetries, and asymptotic behaviors of the Jost solutions and scattering matrix. We also formulate the inverse scattering problem using the matrix Riemann–Hilbert problem (RHP). Furthermore, utilizing the loop group theory, we construct the multi-fold Darboux transformation (DT) within the framework of the robust inverse scattering transform. Additionally, we develop the corresponding Bäcklund transformation (BT) to obtain the multi-fold lattice soliton solutions. To derive the high-order rational solutions, we further construct the high-order DT. Finally, we theoretically and graphically analyze these solutions, which exhibit lattice breather waves, W-shape lattice solitons, high-order lattice rogue waves (RW), and their interactions. [ABSTRACT FROM AUTHOR]

Under investigation in this paper is a (3+1)-dimensional generalized Jimbo–Miwa equation(gJM), which describes many interesting three dimensional nonlinear waves in physics. Based on the properties of the Bell's polynomial, a very classic method is presented to find the Hirota bilinear form of the equation. By using the resulting bilinear form, we systematically construct its lump solutions and lump-like solutions including lump-kink solutions and periodic lump solutions with their corresponding limitations. Moreover, we show that the conditions satisfying by lump solutions are considered to satisfy several important properties, including localization, positive and analyticity. The interaction solutions among a lump and a kink wave are also provided by considering a special function. The corresponding interaction phenomenon does not possess elasticity, but has a constantly removing process between a lump and a kink wave. Finally, periodic lump solutions are also derived by employing the three-wave method. It is hoped that our results can help rich the dynamic behaviors of the (3+1)-dimensional Jimbo–Miwa-like equations. [ABSTRACT FROM AUTHOR]

In this paper, the inverse scattering transform of a two-component modified Korteweg–de Vries equation is under investigation, which is one of the important nonlinear models in mathematics and physics. The spectral analysis with a 4 × 4 Lax pair is performed for the two-component modified Korteweg–de Vries equation, from which a Riemann Hilbert problem is strictly formulated. Moreover, multi-soliton solutions to the two-component modified Korteweg–de Vries equation are obtained through a particular Riemann–Hilbert formulation. Finally, some figures are presented to reveal the soliton features of the two-component modified Korteweg–de Vries equation. [ABSTRACT FROM AUTHOR]

In this work, we consider the generalized (3 + 1)-dimensional Boussinesq equation, which can describe the propagation of gravity wave on the surface of water. Based on the Bell polynomial theory, a powerful technique is employed to explicitly construct its bilinear formalism and two-soliton solutions, based on which the new rational solution is well-constructed. Moreover, the extended homoclinic test approach is presented to succinctly construct the breather wave and rogue wave solutions of the Boussinesq equation. Then the main characteristics of these solutions are graphically discussed. More importantly, they reveal that the extreme behavior of the breather wave can give rise to the rogue wave. [ABSTRACT FROM AUTHOR]

In this work, we investigate the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation in fluid dynamics, which plays an important role in depicting weakly dispersive waves propagated in a quasi-media and fluid mechanics. By employing Hirota's bilinear method, we derive the one- and two-soliton solutions of the equation. Moreover, we reduce those soliton solutions to the periodic line waves and exact breather waves by considering different parameters. A long wave limit is used to derive the rogue wave solutions. Based on the resulting bilinear representation, we introduce two types of special polynomial functions, which are employed to find the lump solutions and interaction solutions between lump and stripe soliton. It is hoped that our results can be used to enrich dynamic behaviours of the (3+1)-dimensional BKP-type equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the non-linear Schrödinger equation in fibers with the presence of group velocity dispersion, selfphase modulation and second-order dispersion terms. Using the ansatz method, we derive its bright, dark, complexitons, Gaussian, and traveling wave solitons, respectively. Moreover, we provide the graphical analysis of some solutions in order to better understand their dynamical behavior. [ABSTRACT FROM PUBLISHER]