N-wave solution of modified Burgers equation

Abstract The modified Burgers equation u t + u n u x = δu xx 2 , where n ≥ 2 is even, is treated analytically for N-wave initial conditions. An exact asymptotic solution is presented, extending the validity of the linear solution far back in time.

[1]  R. E. Grundy,et al.  Nonlinear Diffusion Phenomenon , 1994 .

[2]  E. Suhubi,et al.  Wave Propagation in Dissipative or Dispersive Non-linear Media , 1978 .

[3]  D. Crighton,et al.  Nonlinear wave motion governed by the modified Burgers equation , 1987, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[4]  G. A. Nariboli,et al.  A New Type of Burgers' Equation , 1973 .

[5]  S. Harris,et al.  Sonic shocks governed by the modified Burgers' equation , 1996, European Journal of Applied Mathematics.

[6]  K. T. Joseph,et al.  Exact N-wave solutions for the non-planar Burgers equation , 1994, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[7]  C. Dawson Godunov-mixed methods for advective flow problems in one space dimension , 1991 .