Solitons and Other Solutions for Two Higher-Order Nonlinear Wave Equations of KdV Type Using the Unified Auxiliary Equation Method
E. Zayed, R. Shohib
Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
Received: February 7, 2018; revised version May 8, 2019; in final form May 12, 2019
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Many new types of Jacobi-elliptic function solutions, solitons, and other solutions for two nonlinear partial differential equations, namely, the higher-order wave equation of KdV type (III) and the higher-order wave equation of KdV type (II) have been found using the unified auxiliary equation method combined with the conformable space-time fractional derivatives. The solitary wave solutions and the periodic wave solutions are obtained from the Jacobi elliptic function solutions when its moduli m=1 or m=0, respectively. Comparison of our new results with the well-known results are given.

DOI:10.12693/APhysPolA.136.33
topics: the unified auxiliary equation method combined with the conformable space-time fractional derivatives, exact solutions, periodic solutions, the higher-order wave equation of KdV type (III), the higher-order wave equation of KdV type (II)