Solitons, Cnoidal Waves, Snoidal Waves and Other Solutions to Whitham-Broer-Kaup System

Abstract

Using a computerized symbolic computation technique based on improved Jacobi elliptic function method, we find several solutions for Whitham-Broer-Kaup-Like (WBKL) system. These solutions contain hyperbolic, triangular solutions. When the parameters are taken as special values the solitary wave solutions can be obtained for other systems. The traveling wave solutions are also discussed that obtains solitary wave and singular soliton solution.Keywords: Jacobi elliptic functions method, Nonlinear physical phenomena, Broer-Kaup (BK) system, Whitham-Broer-Kaup-Like system, Whitham-Broer-Kaup system, the classical long-wave system, the variant Boussinesq system and the dispersive long wave system

A linearly implicit conservative difference scheme for the generalized Rosenau–Kawahara-RLW equation

“…Besides all the literature mentioned in the above, there are also a lot of related references which used both analytical and numerical methods to study different nonlinear models. For example, Triki et al [54] discussed the solitary solution for the Gear-Grimshaw model, Bhrawy et al [55] provided solitons, cnoidal waves and snoisal waves for the Whitham-Broer-Kaup system, while Shokri et al [58] numerically solved the two-dimensional complex Ginzburg-Landau equation by using the meshless radial basis functions method, and Dehghan et al [59] applied a semi-analytical method for solving the Rosenau-Hyman equation. Readers can refer to [54][55][56][57] for more discussions on analytically finding solitons and other wave solutions for different nonlinear models, and refer to [58][59][60] for more discussions on numerical studies.…”

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

“…Besides the references mentioned in the above section, there are a lot of related references which used different methods to find the solitons and other wave solutions for different nonlinear models. For example, [54] discussed the solitary solution for the Gear-Grimshaw model, [55] provided solitons, cnoidal waves and snoidal waves for the Whitham-Broer-Kaup system, while [56] gave the solitons and other solutions to the (3+1)-dimensional extended Kadomtsev-Petviashvili equation with power law nonlinearity. Readers can refer to [54][55][56][57][58][59][60][61][62][63] for more discussions on finding solitons and other wave solutions for different nonlinear models.…”

“…From (55) and the definition of the · -norm, one can see that (55) has only a trivial solution. Thus, (36) determines U n+1 uniquely.…”

Reproducing Kernel Hilbert Space Method]{representation for the Reproducing Kernel Hilbert Space Method for a Nonlinear System

“…Ordinary differential systems are important for actual-physical problems. These systems were used for a lot of problems [4][5][6]12]. Biswas et al investigated systems by some varied techniques [7].…”