Analytical Solutions of Nonlinear Wave Equations Using Symbolic Computation: A MathHandbook-Based Approach

We present a computational framework for deriving and verifying analytical solutions of nonlinear wave equations using the symbolic system MathHandbook.com. The nonlinear PDE
y_tt – Δy + c y^2 = 0
is reduced via automated Lie symmetry methods, yielding ordinary differential equations solvable in terms of Weierstrass elliptic functions. The workflow integrates PDE-to-ODE reduction, symbolic integration, solution reconstruction, and verification through symbolic residuals and numerical sampling. This demonstrates the role of symbolic computation as both an analytical engine and a diagnostic tool, complementing numerical simulation in mathematical physics. We found relationship between defocusing and focusing solutions.

nonlinear wave equation, Analytical Solutions, Symbolic Computation

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