Fully integrable one-dimensional nonlinear wave equation: Solution of a general initial value problem

Abstract

A new integrable case of the one-dimensional nonlinear wave equation was found. A general solution for this case depending on two arbitrary functions was derived. The functional form of the speed of sound can be used to model weak nonlinear waves in non-dispersive media. For the initial value problem the nonlinear generalization of the d’Alembert’s formula was obtained.

Keywords

• Exact solutions
• General solution
• Wave equation
• Arbitrary functions
• Riemann invariants
• Nonlinear waves