Abstract
Abstract In applied mathematics, physics, and mechanics, many mathematical models are established in the form of nonlinear wave equations. Therefore, a method for studying traveling wave solutions of nonlinear wave equations based on functional analysis is proposed. The boundary value stability of the nonlinear second order nonlinear wave equation is modified by using functional analysis of multiple variables. In this paper, a new integral term is introduced into the organization mapping functional, the concept and construction of the nonlinear wave equation are analyzed, and its continuity is proved. According to the growth order of the traveling wave solution of nonlinear wave equation, the method of finding the traveling wave solution and its stability are studied.
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