Numerical studies of the regularized long-wave (RLW) equation u t+ux+(6u2-uxt)x=0 suggests it has a two-soliton solution although an analytic form for this has not yet been found. The authors show that a modified form of the RLW equation ut+ux+(4u2+2wxvt-u xt)x=0, with u=wt=vx, has an exact two-soliton solution. The modified equation has the same solitary-wave solution as the original equation and its analytic two-soliton solution agrees closely with the numerical solution of the RLW equation.
|Journal||Journal of Physics A: Mathematical and General|
|Publication status||Published - 1976|