In this paper, the tanh and sine–cosine methods are used to construct exact periodic and soliton solutions of nonlinear evolution equations arising in mathematical physics. Many new families of exact travelling wave solutions of the generalized Hirota–Satsuma coupled KdV system, generalized-Zakharov equations and (2 + 1)-dimensional Broer–Kaup– Kupershmidt system are successfully obtained. The ...

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...

a modified f-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (nlpdes) is discussed. we use this method to construct many new solutions to the nonlinear whitham-broer-kaup system (1+1)-dimensional. the solutions obtained include jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

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...

This paper discusses several algorithmic ways of constructing integrable evolution equations based on Lie algebraic structure. We derive, in a pedagogical style, a large class of two component peakon type dual systems from their two component soliton equations counter part. We study the essential aspects of Hamiltonian flows on coadjoint orbits of the centrally extended semidirect product group...

In this short note, we discuss a new formula for solving the nonlocal $$\overline{\partial }$$ -problem, and application to Manakov–Zakharov dressing method. We then explicitly apply complex (2+1)D Kadomtsev–Petviashvili equation completely integrable generalization of Kaup–Broer (or Kaup–Boussinesq) system. will also how real (1+1)D solutions are expressed using formalism. It is simple express...

In this paper, the projective Riccati equation method is applied to find exact solutions for fractional partial differential equations in the sense of modified RiemannLiouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the vali...

In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham–Broer–Kaup equations. The explicit approximate traveling solutions are obtained by using this method. The efficiency and accuracy of the present method is demonstrated by two aspects. One is analyzing the approximate solutions graphically. The other is compari...