New exact wave solutions to the space-time fractional-coupled Burgers equations and the space-time fractional foam drainage equation

Figures & data

Figure 1. Modulus plot of kink wave shape of $u_2$ when r₁ = 1.2, A = C = E = m = 1, $\sqrt{\mathrm{\Omega }}=2,\psi =A-C,B=a_0=0,p=1.1,q=1.5$ and $-10\le x,t\le 10$.

Figure 2. Modulus plot of singular kink wave shape of $u_1$ when r₂ = 1.2, A = C = E = m = 1, $\sqrt{\mathrm{\Omega }}=2,\psi =A-C,B=a_0=0,p=1.1,q=1.5$ and $-10\le x,t\le 10$.

Figure 3. Modulus plot of singular kink wave shape of $u_1$ when r₂ = 1.2, C = E = m = 1, $\sqrt{\mathrm{\Omega }}=2,\psi =A-C,A\ne 1,B=0,a_0=0,p=1.1,q=1.5$ and $-10\le x,t\le 10$.

Figure 4. Modulus plot of singular periodic wave shape of $v_8$ when A = 3, r₂ = 1.2, C = E = m = B = 1, $\sqrt{-\mathrm{\Delta }}=-2,\psi =A-C,a_0=0,p=1.1,q=1.5$ and $-10\le x,t\le 10$.

Figure 5. Modulus plot of singular periodic wave shape of $v_9$ when A = 3, r₁ = 1.2, C = E $=m=B=1,\sqrt{-\mathrm{\Delta }}=-2,\psi =A-C,a_0=0,p=1.1,q=1.5$ and $-10\le x,t\le 10$.

Figure 6. Modulus plot of singular kink wave shape of $u_5$ when A = 3, C = E $=m=B=1,\psi =A-C,a_0=0,p=1.1,q=1.5$ and $-10\le x,t\le 10$.

Figure 7. Modulus plot of kink wave shape of $w_2$ when $A=3,r_1=1.2,C=E=m=B=1,\sqrt{\mathrm{\Omega }}=2,\psi =A-C$ and $-10\le x,t\le 10$.

Figure 8. Modulus plot of kink wave shape of $w_1$ when $A=3,r_2=1.2,C=E=m=B=1,\sqrt{\mathrm{\Omega }}=2,\psi =A-C$ and $-10\le x,t\le 10$.

Figure 9. Modulus plot of singular periodic wave shape of $w_8$ when A = 3, r₂ = 1.2,  $C=E=m=B=1,\sqrt{-\mathrm{\Delta }}=-2,\psi =A-C$ and $-10\le x,t\le 10$.

Figure 10. Modulus plot of singular kink wave shape of $w_5$ when A = 3, C = E = m = B = 1,$\psi =A-C$ and $-10\le x,t\le 10$.