A new three-wave method is efficient and well-developed approach to solve nonlinear partial differential equation. In this paper, a (3+1)-dimensional Jimbo-Miwa equation is investigated by using this approach. Some periodic wave solutions and kink solutions are obtained through the Hirota bilinear form. Furthermore, figures of some special periodic wave solutions and kink solutions are presented to illustrate the dynamical features of these solutions.where f = f (x, y, z, t) is also real function with respect to variables x, y, z and t. D 3x D y , D t D y and D x D z are called Hirota bilinear operators [23] defined by Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

<abstract><p>In this paper, we are concerned with the existence of nontrivial positive solutions for the following generalized quasilinear elliptic equations with critical growth</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} -{\rm{div}}(g^{p}(u)|\nabla u|^{p-2}\nabla u)+ g^{p-1}(u)g'(u)|\nabla u|^{p}+ V(x)|u|^{p-2}u = h(x, u), \; \; x\in \mathbb{R}^{N}, \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>where $ N\geq3 $, $ 1 &lt; p &lt; N $. Under some suitable conditions, we prove that the above equation has a nontrivial positive solution by variational methods. To some extent, our results improve and supplement some existing relevant results.</p></abstract>

<abstract><p>In this paper, we study the existence of a positive ground state solution for a class of generalized quasilinear Schrödinger equations with asymptotically periodic potential. By the variational method, a positive ground state solution is obtained. Compared with the existing results, our results improve and generalize some existing related results.</p></abstract>