Theta Function Solutions of the 3 + 1‐Dimensional Jimbo‐Miwa Equation

Abstract

The 3 + 1-dimensional Jimbo-Miwa equation can be written into a Hirota bilinear form by the dependent variable transformation. We give its one-periodic wave solution and two-periodic wave solution by utilizing multidimensional elliptic Θ-function. With the help of the solution curves, the asymptotic properties of the periodic waves are analyzed in detail.

Classification of All Single Traveling Wave Solutions of ( 3 + 1 )-Dimensional Jimbo-Miwa Equation with Space-Time Fractional Derivative

“…In 2016, Ma gets four kinds of block solutions for Hirota bilinear form which are given in [20]. In 2017, Su and Dai [21] gave its single-periodic wave solution and doubleperiodic wave solution by using the multidimensional elliptic function. It is worth mentioning that with the development of traveling wave solution theory, more and more effective methods are applied to find traveling wave solutions.…”