1. These conclusions are useful to optimise the design of the solitary wave transmission system near zero-dispersion.

2. The existence of smooth solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions has then proved.

3. The wave from vessel's launch causes crack of mooring chain for fixing pontoon and is considered to be solitary wave through analyses.

4. Under various parameter conditions, all exact explicit formulas of solitary wave solutions and kink (anti-kink) wave solutions and uncountable infinity many periodic wave solutions are listed.

5. 21 Under various parameter conditions, all exact explicit formulas of solitary wave solutions and kink (anti-kink) wave solutions and uncountable infinity many periodic wave solutions are listed.

6. When the integral constant is zero, the existence of smooth solitary wave solutions, uncountably infinite, many smooth periodic wave solutions, and kink and anti-kink wave solutions are proved.

7. Starting from an integrated form of the system of governing equations in terms of pseudopotential, higher order nonlinear and dispersive effects are obtained for an ion-acoustic solitary wave.

8. When a sound wave strikes the spheres at one end of the acoustic lens, the sound gets converted into a type of shock wave known as a solitary wave.