Nonlinear delay reaction-diffusion equations: Traveling-wave solutions in elementary functions

作者：Polyanin Andrei D^*; Sorokin Vsevolod G

来源：Applied Mathematics Letters, 2015, 46: 38-43.

DOI：10.1016/j.aml.2015.01.023

• Delay reaction-diffusion equations
• Nonlinear delay differential equations
• Exact solutions
• Traveling-wave solutions
• Solutions in elementary functions

The paper deals with nonlinear delay reaction-diffusion equations of the form
u(t) = au(xx) + F(u, (u) over bar),
where u = u(x, t) and (u) over bar = u(x, t - tau), with tau denoting the delay time. We present a number of traveling-wave solutions of the form u = w(z), z = kx+lambda t, that can be represented in terms of elementary functions. We consider equations with quadratic, power-law, exponential and logarithmic nonlinearities as well as more complex equations with the kinetic function dependent on one to four arbitrary functions of a single argument. All of the solutions obtained involve free parameters and so may be suitable for solving certain model problems as well as testing numerical and approximate analytical methods for delay reaction-diffusion equations and more complex nonlinear delay PDEs.

• 出版日期2015-8