One of the fascinating aspects of nonlinear differential equations is the existence of solitary wave solutions, which are waveforms that maintain their shape while traveling at constant speed.

which can complicate numerical solutions. This method has been tested for various equations, including the wave, heat, and Poisson equations, and has proven effective in applications requiring ...

equations with both vanishing and nonvanishing boundary conditions at infinity; solitons and rogue wave solutions; vector soliton interactions, etc. Other integrable systems I have studied over the ...

The wave equation is a very important formula that is often used to help us describe waves in more detail. It should be noted that some particular waves have their own specific speeds. The speed ...