Nonlinear differential equations are known to describe a wide variety of phenomena not only in physics, in which applications extend over magnetofluid dynamics, water surface gravity waves, electromagnetic radiation reactions, and ion acoustic waves in plasmas, just to name a few, but also in biology and chemistry. It is one of the important tasks in the study of nonlinear differential equation...

Abstract We analyze the Broer-Kaup system posed on half-line by using unified transform method, also known as Fokas method. derive formal representation of solution for in terms matrix Riemann-Hilbert problem formulated complex plane spectral parameter. The jump is uniquely defined functions that satisfy a certain relation, called global relation involving initial and boundary values. Furthermo...

We take into account here the stochastic-fractional Broer–Kaup equations (SFBKEs) perturbed by multiplicative Wiener process. To get rational, hyperbolic, and elliptic stochastic solutions for SBKEs, we utilize Jacobi function method. The derived are significantly more useful effective in comprehending various important challenging physical phenomena due to of SFBKEs describing propagation shal...

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...

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...

We construct the traveling wave solutions of the 1 1 -dimensional modified Benjamin-BonaMahony equation, the 2 1 -dimensional typical breaking soliton equation, the 1 1 -dimensional classical Boussinesq equations, and the 2 1 -dimensional Broer-Kaup-Kuperschmidt equations by using an extended G′/G -expansion method, where G satisfies the second-order linear ordinary differential equation. By us...

Abstract. Let G be a reductive algebraic group over C and let N be a G-module. For any subspace M of N , the Brylinski-Kostant filtration on M is defined through the action of a principal nilpotent element in LieG. This filtration is related to a q-analog of weight multiplicity due to Lusztig. We generalize this filtration to other nilpotent elements and show that this generalized filtration is...

To study a nonlinear partial differential equation (PDE), the Painlev́e expansion developed by Weiss, Tabor and Carnevale (WTC) is one of the most powerful methods. In this paper, using any singular manifold, the expansion series in the usual Painlev́e analysis is shown to be resummable in some different ways. A simple nonstandard truncated expansion with a quite universal reduction function is u...