Analytical Solutions for the Elastic Circular Rod Nonlinear Wave, Boussinesq, and Dispersive Long Wave Equations

Figure 8

The solitary wave and behavior of the solutions 𝑢(𝑥,𝑦,𝑡)=−1+ tanh(𝑥−2𝑦+𝑡)/(1+sech(𝑥−2𝑦+𝑡))+(1+sech(𝑥−2𝑦+𝑡))/tanh(𝑥−2𝑦+𝑡) for 𝑡=0, −4⩽𝑥⩽4, and −4⩽𝑦⩽4.