Abundant explicit periodic wave solutions and their limit forms to space‐time fractional Drinfel'd–Sokolov–Wilson equation

Abstract

In this paper, we exploit the generalized bifurcation method to study space-time fractional Drinfel'd-Sokolov-Wilson equation and derive its various new exact explicit periodic wave solutions. Especially and interestingly, we find the so-called M/W-shaped periodic wave solutions, which were not found in previous studies. Furthermore, we uncover their inside limit relations as well as their limit relations with other solutions under corresponding parameters conditions. The previous results are extended.

Persistence of Kink and Periodic Waves to Singularly Perturbed Two-Component Drinfel’d–Sokolov–Wilson System

“…The bifurcation method [11] and the Expfunction method [12] were also employed to derive exact solutions of system (1). Additionally, some methods including the modified kudryashov method [13], the first integral method [14] and the bifurcation method [15,16] were extended to find abundant exact solutions of fractional DSW system. However, we find that there is little work concerning singularly perturbed DSW system.…”

Bifurcation analysis and dynamics of abundant traveling waves of the modified Novikov equation

“…Furthermore, how about the dynamics of the waves under general $$$ b $$$? Based on these motivations, we further study Equation () with arbitrary $$$ b\in \mathbb{R} $$$ from the perspective of dynamical systems 24–34 and show that Equation () possesses solitary waves, periodic waves, compactons, kink (antikink), and kink‐like (antikink‐like) waves. The detailed differences of the results between Meng and He 23 and this paper are given in Remark 1.…”