Several Families of New Exact Solutions for Wave-Like Equations with Variable Coefficients

Abstract

AbstractSeveral families of new exact solutions for second-order wave-like partial differential equations with variable coefficients are derived in this paper. To derive these solutions, certain recurrence relations for powers of the variables and coefficients are formed using the method of balancing powers of the variables. Solving these recurrence relations, several exact solutions are derived. We derive all polynomial solutions of these partial differential equations. Different families of new exact solutions of these equations which can be expressed in terms of hypergeometric functions are also constructed. Euler–Tricomi equation, Keldysh equation, and generalized Euler–Tricomi equations are special cases of this general equations.KeywordsExact solutionsPolynomial solutionsHypergeometric functionsWave equationEuler–Tricomi equationKeldysh equation