Remarks on the Fundamental Solution to Schrödinger Equation with Variable Coefficients

Remarks on Fundamental Solutions to Schrödinger Equation with Variable Coefficients

Auxiliary equation method for the mKdV equation with variable coefficients

By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of nonlinear evolution equations with variable coefficients. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients. As a result, new explicit solutions including solitary wave solutions and trigonometric function solutions...

Mackey-glass equation with variable coefficients

is considered, with variable coefficients and a nonconstant delay. Under rather natural assumptions all solutions are positive and bounded. Persistence and extinction conditions are presented for this equation. In the case when there exists a constant positive equilibrium, local asymptotic stability of the constant solution and oscillation about this equilibrium are analyzed. The results are il...

An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

Exact Solutions to a Generalized BBM Equation with Variable Coefficients

An auxiliary equation technique is applied to investigate a generalized Benjamin-Bona-Mahony equation with variable coefficients. Many exact traveling wave solutions are obtained which include algebraic solutions, solitons, solitary wave solutions and trigonometric solutions. Mathematics Subject Classification: 35Q53, 35B35