Kink Waves and Their Evolution of the RLW-Burgers Equation

Table 1

Bounded travelling waves of (1.1) under different parameter conditions.

Probability of parameters				Type of traveling wave
𝑒>0	𝑓>0	𝑔^2−4𝑒≥0	𝑔>0	I
			𝑔<0	II
		𝑔^2−4𝑒<0	𝑔>0	III
			𝑔<0	IV
	𝑓<0	𝑔^2−4𝑒≥0	𝑔>0	II
			𝑔<0	I
		𝑔^2−4𝑒<0	𝑔>0	III
			𝑔<0	IV
𝑒<0	𝑓>0	𝑔^2+4𝑒≥0	𝑔>0	I
			𝑔<0	II
		𝑔^2+4𝑒<0	𝑔>0	III
			𝑔<0	IV
	𝑓<0	𝑔^2+4𝑒≥0	𝑔>0	II
			𝑔<0	I
		𝑔^2+4𝑒<0	𝑔>0	III
			𝑔<0	IV

I: monotone increasing kink wave; II: monotone decreasing kink wave; III: increasing oscillatory kink wave; IV: damped oscillatory kink wave.