Abstract
This paper systematically studies the complete integrability of the Newell equation. Using generalized Bell polynomials, the corresponding bilinear equation, bilinear Bäcklund transformation, Lax pair, and multi-shock wave solutions are successfully obtained. In addition, using the multidimensional Riemann theta functions, the periodic wave solutions of the Newell equation are constructed. On this basis, the asymptotic behavior of the periodic wave solution is given, which is the relationship between the periodic wave solution and the solitary wave solution.
Highlights
Since the pioneering introduction of solitons into nonlinear science, many experts and scholars have studied and explored its various aspects
This paper systematically studies the complete integrability of the Newell equation
Nakamura proposed a synthetic approach for constructing multi-periodic wave solutions of nonlinear equations based on the Hirota bilinear method
Summary
Since the pioneering introduction of solitons into nonlinear science, many experts and scholars have studied and explored its various aspects. Nakamura proposed a synthetic approach for constructing multi-periodic wave solutions of nonlinear equations based on the Hirota bilinear method. The advantage of this method is that it only depends on the bilinear form. To solve this problem, Lambert et al introduced the concept of the Bell polynomials in algebra to nonlinear differential equations, which made it simple to construct bilinear forms of nonlinear equations [9]. Lambert et al introduced the concept of the Bell polynomials in algebra to nonlinear differential equations, which made it simple to construct bilinear forms of nonlinear equations [9] This method simplifies the computational complexity but is practical.
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