1. Solitons are solitary waves; the Severn bore is a good example.

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

3. The solitary wave theory of the weakly nonlinear, non-axisymmetric disturbances is used to model the spiral vortex breakdown.

4. These solutions contain solitary wave solutions, triangular periodic solutions and so on.

5. Single solitary wave solutions, multi-solitary wave solutions and exponential localized solitary wave solutions can be constructed from the results.

6. The phenomenon of solitary wave generated by the ship in shallow water can be observed.

7. Thirdly, the two-dimensional numerical model of solitary wave and regular wave slamming to leveling board is built on the basis of SPH method.

8. By introducing double parameter transformation, the explicit solitary wave solutions for a nonlinear equation are obtained.

9. These solutions may be reduced to the envelope solitary wave solutions under some conditions.

10. And the envelope solitary wave solutions and envelope sinusoidal wave solutions have been obtained.

11. Then ten new real exact solitary wave solutions for then-dimension nonlinear Chaffe-Infante equation are obtained by using these formulas and a direct supposal method.

12. In this paper new exact solitary wave solutions of some nonlinear evolution equations are constructed by replacing the hyperbola function with the combinations of the exponential functions.

13. The reflection coefficient of a solitary wave decreases as the effective porosity increases for a given permeability coefficient.

14. The results show that the present approach is valid for modeling the propagation of a solitary wave.

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

16. 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.

17. 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.

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18. In this paper the numerical study was conducted to simulate the whole process of solitary wave overtopping a sloping bank.

19. 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.

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

21. The results showed that the oscillation of the adatom cells with the magnitude of micrometer order on Cu alloy exhibits the features of the solitary wave of pseudo-fluids tate.

22. As taking account of high order expanded terms, there exists no solitary wave in beam propagation by numerical analysis without or with absorption, and the beams are controlled by input intensity.

23. The extended homogenous balance method is applied to find solitary wave solutions of nonlinear evolution equations.

24. If the effective porosity is given, the reflection coefficient of a solitary wave decreases also as the permeability coefficient increases.

25. This method also can be used to find new solitary wave solutions to other nonlinear evolution equations.

26. In this paper, the effect of dust size distribution for the dust acoustic solitary wave (DASW) in the cold dusty plasma, the hot dusty plasma, the magnetized dusty plasmas and the dusty pl.

27. By the orbit in the phase portraits, different kinds of solitary wave, kink wave and periodic wave solutions are obtained.

28. The system is solved by using Wu Elimination and exact solitary wave solutions of nonlinear evolution equations are then obtained.

29. The results show that the present NWT can simulate the propagation of a solitary wave and nonlinear periodic waves over gentle beaches efficiently with good stability.