Consistent Burgers equation expansion method and its applications to high- dimensional Burgers-type equations

Abstract

In this paper, a novel method, named as consistent Burgers equation expansion (CBEE) method, is proposed to solve nonlinear evolution equations (NLEEs) by the celebrated Burgers equation. NLEEs are said to be CBEE solvability, if it satisfied the CBEE method. In order to verify the effectiveness of the CBEE method, we take (2+1)-dimensional Burgers equation as a example. From the (1+1)-dimensional Burgers equation, many new explicit solutions of the (2+1)-dimensional Burgers equation are derived. The obtained results illustrate that this method can be effectively extended to other NLEEs.

Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

“…3. Three solitonic families for equation (1), their difference and experimental support 7 3.1. Three explicitly-solvable solitonic families for equation (1) We now choose that…”

“…Nonlinear waves are physically and currently interesting [1][2][3]. Physical studies on the pulse waves in the human arteries have started from the ancient times until the present, while recent theoretical efforts have been focused on the probes for nonlinear pulse waves in the variable-radius arteries [4][5][6][7][8][9][10][11][12][13][14][15][16].…”