New traveling wave structures for two higher dimensional nonlinear evolution equations with time-dependent coefficients: Horseshoe-like solitons and multiwave interaction solutions

In this paper, by introducing new traveling wave transformations in specific nonlinear forms, a variety of new multiwave interaction solutions for two higher dimensional nonlinear evolution equations with time-dependent coefficients are investigated. These new kinds of multiwave solutions can enrich solutions of nonlinear evolution equations with variable coefficients.

Rogue waves generation and interaction of multipeak rational solitons in the system of equations for the ion sound and Langmuir waves

In this paper, our purpose is to construct multiwave solutions for the system of equations for the ion sound and Langmuir waves (SEISLWs) by utilizing the traveling wave and logarithmic transformation with the help of symbolic computation and the ansatz function method. We apply three distinctive approaches: namely, positive quadratic function approach, three waves approach and double exponential approach. By choosing suitable parametric values, 3D graphics are plotted to get different types of multiwave solutions including lump waves, rogue wave and multipeak soliton solutions. Moreover, we revealed very interesting multiwaves interactional phenomena.

Traveling Wave Solutions and Infinite-Dimensional Linear Spaces of Multiwave Solutions to Jimbo-Miwa Equation

The traveling wave solutions and multiwave solutions to (3 + 1)-dimensional Jimbo-Miwa equation are investigated in this paper. As a result, besides the exact bounded solitary wave solutions, we obtain the existence of two families of bounded periodic traveling wave solutions and their implicit formulas by analysis of phase portrait of the corresponding traveling wave system. We derive the exact 2-wave solutions and two families of arbitrary finiteN-wave solutions by studying the linear space of its Hirota bilinear equation, which confirms that the (3 + 1)-dimensional Jimbo-Miwa equation admits multiwave solutions of any order and is completely integrable.