Study On Solitary Wave Solution Of KdV Equation In Marine Environment

In recent years,because the basic equations used in many natural science researches are common partial differential equations,partial differential equations have received extensive attention in scientific research fields such as computational mathematics,physical oceanography,and engineering applications.However,the analytical solutions of most partial differential equations are complex and have low applicability.Therefore,how to achieve more reasonable numerical solutions for partial differential equations has become a focus of attention in various research fields.This article mainly studies the partial differential equation for controlling internal waves in the ocean-the Kd V equation,and uses a variational integration method to solve the numerical solution of the partial differential equation to construct and solve the third-order numerical format of the Kd V equation.The constructed numerical format exhibits various advantages,including clear physical meaning,conservation of the format,and diversity of formats,making it an ideal solution A numerical method that can construct discrete formats according to specific accuracy requirements.Then,the propagation process of solitary wavelet in Kd V theory is numerically simulated.The specific research content of this article is as follows:Firstly,this article introduces the Taylor formula method,which is convenient for obtaining and analyzing the error accuracy of its discrete format.It can construct a discrete format with order accuracy based on any given partial differential equation,and combine Taylor fitting function and variational integral method to study the construction of numerical format for third-order partial differential equation.For the Kd V equation,a new numerical format is constructed to verify its accuracy as fourth order in space and second order in time.Then the error and convergence order,as well as the conserved quantity of single wave and double wave cases,are discussed in the numerical experiments,and the convergence and conservation of the numerical scheme are verified according to the experimental results.Finally,based on the classic simple Kd V equation and the theory of Kd V equation under the action of multiple factors,the propagation process of soliton internal waves in bottomless and sloped bottom terrain is numerically simulated.According to the results,the variation characteristics of various related physical quantities of soliton in the propagation process are investigated,which provides a reference for the subsequent research on the numerical model of Kd V equation in the marine environment.