The Harry Dym equation, which is related to the classical string problem, is derived in three different ways. An implicit cusp solitary-wave solution is constructed via a simple direct method. The existing connections between the Harry Dym and the Kortwegde Vries equations are uniformised and simplified, and transformations between their respective solutions are carried out explicitly. Whenever...

A cascade algorithm for solitary-wave solutions to the Benjamin equation is conctructed, implemented and analyzed both numerically and theoretically. The major advantages over the existing homotopy algorithm are its simplicity, eeciency, generality, and the many properties it reveals about the exact solution, whose closed form is out of our reach.

Based on the extended hyperbolic functions method, we obtain the multiple exact explicit solutions of the Klein–Gordon–Zakharov equations. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for u and n, (b) the solitary wave solutions of kink-type for u and bell-type for n, (c) the solitary wave solutions of a compound of the bell-type and the kink-type fo...

The solitary water wave problem is to find steady free surface waves which approach a constant level of depth in the far field. The main result is the existence of a family of exact solitarywaves of small amplitude for an arbitrary vorticity. Each solution has a supercritical parameter value and decays exponentially at infinity. The proof is based on a generalized implicit function theorem of t...

A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary waves within this family for wide range of parameter values. PACS codes: 02.30.Jr; 47.50.Cd; 83.10.Gr

We derive a general theorem relating the energy and momentum with the velocity of any solitary wave solution of the generalized KdV equation in N -dimensions that follows from an action principle. Further, we show that our N -dimensional Lagrangian formulation leads to a subclass of the equations discussed recently by Rosenau, Hyman and Staley.

Solitary wave is a permanent when the dissipation ignored. Many analytical solutions have been developed for finite amplitude solitary waves. In additional to perturbation solutions, closed form are also available (e.g., McCowan 1891, Clamond and Fructus 2003, being denoted as CF from hereon), which more accuracy, especially larger waves were discussed in Wang Liu (2022). (2022) ’s laboratory e...

New analytic sech2-type traveling solitary-wave solutions, satisfying zero background at infinity, of a general fifth-order shallow water-wave model are found and compared with previously obtained non-zero background solutions. The allowed coefficient regions for the solitary-wave solutions are classified by requiring the wave number and angular frequency to be real. Detailed numerical simulati...

Long surface gravity waves of finite amplitude in uniform shear flows are considered by using an asymptotic model derived under the assumption that the aspect ratio between wavelength and water depth is small. Since its derivation requires no assumption on wave amplitude, the model can be used to describe arbitrary amplitude waves. It is shown that the simple model captures the interesting feat...

We derive the properties of self-induced transparency ~SIT! solitary waves in a one-dimensional periodic structure doped uniformly with resonance two-level atoms. In our model, the electromagnetic field is treated classically and the dopant atoms are described quantum mechanically. The resulting solitary waves take the form of ultrashort ~picosecond! laser pulses which propagate near the band e...