Exact solutions of (3 +1)-dimensional nonlinear evolution equations

Exact Solutions for Some (2+1)-Dimensional Nonlinear Evolution Equations by Using Tanh-coth Method

In this work, we established exact solutions for some nonlinear evolution equations. The tanhcoth method was used to construct solitary and soliton solutions of (2+1)-dimensional nonlinear evolution equations. The tanh-coth method presents a wider applicability for handling nonlinear wave equations.

Exact solutions of nonlinear interval Volterra integral equations

Study of Integrability and Exact Solutions for Nonlinear Evolution Equations

and Applied Analysis 3 Two papers in our special issue are concerned about the study of application to the symbolic computation method and special function. In the paper titled “New nonlinear systems admitting Virasoro-type symmetry algebra and groupinvariant solutions” by L. Wang et al., the authors extend the application of Virasoro-type symmetry prolongationmethod to coupled systems with two...

Exact traveling wave solutions of some nonlinear evolution equations

Using a traveling wave reduction technique, we have shown that Maccari equation, (2?1)-dimensional nonlinear Schrödinger equation, medium equal width equation, (3?1)-dimensional modified KdV–Zakharov– Kuznetsev equation, (2?1)-dimensional long wave-short wave resonance interaction equation, perturbed nonlinear Schrödinger equation can be reduced to the same family of auxiliary elliptic-like equ...

Exact traveling wave solutions for system of nonlinear evolution equations

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolu...

Extended Gram-type determinant, wave and rational solutions to two (3+1)-dimensional nonlinear evolution equations

New exact Grammian determinant solutions to two (3+1)-dimensional nonlinear evolution equations are derived. Extended set of sufficient conditions consisting of linear partial differential equations with variable-coefficients is presented. Moreover, a systematic analysis of linear partial differential equations is used for solving the representative linear systems. The bilinear Bäcklund transfo...