New Non-Travelling Wave Solutions of Calogero Equation

In this paper, the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation. The equation is reduced to some (1+1)-dimensional nonlinear equations by applying the variable separation approach and solves reduced equations with the extended homoclinic test technique. Based on this idea and with the aid of symbolic computation, some new explicit solutions can be obtained.

Painlevé Integrability and a New Exact Solution of the Multi-Component Sasa-Satsuma Equation

In this article, Painlevé integrability of the multi-component Sasa-Satsuma equation is confirmed by using the standard WTC approach and the Kruskal simplification. Then, by means of the multi-linear variable separation approach, a new exact solution with lower-dimensional arbitrary functions is constructed. For the physical quantity $U\; = \;\sum\nolimits_{i\; = \;1}^N \sum\nolimits_{j\; = \;i}^N {a_{ij}}{p_i}{p_j}\; = \; - \;\frac{3}{{2\beta }}\frac{{{F_x}{G_y}}}{{{{(F\; + \;G)}^2}}},$ new coherent structure which possesses peakons at x-axis and compactons at y-axis is illustrated both analytically and graphically.

Application of the Improved Mapping Approach to Exact Solutions and Chaotic Patterns for a Nonlinear Equation

Starting from an improved mapping approach and a linear variable separation approach, a series of exact solutions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli system (BLMP) is derived. Based on the derived variable separated solution, we obtain some special localized excitations such as dromion, solitoff and chaotic patterns.

Riccari Equation Expansion Approach to Construct Complex Wave Solutions for the Related Schrödinger Equation

Starting from the Riccari equation()expansion approach and a linear variable separation approach, some new complex wave solutions with of the related SchrÖdinger (RS) equation,are derived.

Classification and Approximate Functional Separable Solutions to the Generalized Diffusion Equations with Perturbation

In this paper, the generalized diffusion equation with perturbation ut = A(u;ux)uII+eB(u;ux) is studied in terms of the approximate functional variable separation approach. A complete classification of these perturbed equations which admit approximate functional separable solutions is presented. Some approximate solutions to the resulting perturbed equations are obtained by examples.

New Mapping Solutions and Line Soliton Excitations in a (1+1)-Dimensional Dispersive Long-Water Wave System

With the help of the symbolic computation system Maple and the mapping approach and a linear variable separation approach, a new family of exact solutions of the (1+1)-dimensional dispersive long-water wave system (DLWW) is derived. Based on the derived solitary wave solution, some novel localized excitations are investigated.

Extended Mapping Approach and Exact Solutions for a (1+1)-Dimensional Benjamin-Boma-Mahony Equation

With the help of the symbolic computation system Maple and the extended mapping approach and a linear variable separation approach, a new family of exact solutions (including the solitary wave solutions, periodic wave solutions and rational function solutions) of the (1+1)-dimensional Benjamin-Boma-Mahony (BBM) equation is derived.

Study of the Exact Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

With the help of the symbolic computation system Maple and the (G'/G)-expansion approach and a special variable separation approach, a series of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave solution, some novel domino solutions and chaotic patterns are investigated.

Approximate Functional Variable Separation for the Quasi-Linear Diffusion Equations withWeak Source

As an extension to the functional variable separation approach, the approximate functional variable separation approach is proposed, and it is applied to study the quasi-linear diffusion equations with weak source. A complete classification of these perturbed equations which admit approximate functional separable solutions is obtained. As a result, the corresponding approximate functional separable solutions to the resulting perturbed equations are derived via examples.

Bell Waves and Kind Waves for a (1+1)-Dimensional Nonlinear Partial Differential Equation

With the help of the symbolic computation system Maple and the mapping approach and a linear variable separation approach, a new family of exact solutions of the (1+1)-dimensional Burgers system is derived. Based on the derived solitary wave solution, some novel bell wave and kind wave excitations are investigated.