solitary wave solutions to the broer-kaup equations and approximate long water wave equa-tions are considered challenging by using the rst integral method.the exact solutions obtainedduring the present investigation are new. this method can be applied to nonintegrable equa-tions as well as to integrable ones.

We derive the Whitham modulation equations for nonlinear Schr\odinger equation in plane (2d NLS) with small dispersion. The are derived terms of both physical and Riemann variables; latter yields hydrodynamic type. complete 2d NLS system consists six dynamical evolutionary form two constraints. As an application, we determine linear stability one-dimensional traveling waves. In elliptic hyperbo...

In this article, the exact solutions of stochastic conformable Broer–Kaup equations with derivatives which describe bidirectional propagation long waves in shallow water are obtained using modified exponential function method and generalized Kudryashov method. These consist hyperbolic, trigonometric, rational solutions, respectively. This shows that proposed methods competent sufficient. additi...

The Broer-Kaup equation is one of many equations describing some phenomena shallow water wave. There are errors in scientific research because the existence non-smooth boundaries. In this paper, we generalize to fractal space and establish variational formulations through semi-inverse method. acquired formulation reveals conservation laws an energy form suggests possible solution structures mor...

A complete set of conditions describing the transition across the dissipationless undular bore (dispersive shock) is derived for nonlinear weakly dispersive conservative systems that generally are not integrable by the inverse spectral transform method. In the absence of integrable structure, we postulate modulation description of the undular bore with the aid of the averaged Whitham equations ...

We study the Cauchy problem for the Whitham modulation equations for monotone increasing smooth initial data. The Whitham equations are a collection of one-dimensional quasi-linear hyperbolic systems. This collection of systems is enumerated by the genus g=0,1,2, . . . of the corresponding hyperelliptic Riemann surface. Each of these systems can be integrated by the so called hodograph transfor...