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ties. They showed how the ion fluid temperature modifies the DIAWs

properties.

1.9 Nonlinear Waves

There are variety of waves that driven by nonlinear mechanisms. For

wave with large amplitudes, the nonlinearity effects cannot be ignored. In

plasmas, the nonlinearity contribution is to localize the waves, leading to

different types of waves such as solitons, shock and rogue wave structures,
etc. Therefore, we will give a short note to some of these waves.

1.9.1 Solitary Waves Solitons

Solitary wave propagates without any change in shape or size with

wave group velocity. Envelope of these waves have one peak and arises in

different areas e.g. surface water wave, intensity of light in optical fibers

and fluids.
The soliton was first described by Scottish scientist and engineer, John

Scott Russell in 1834 in Union Canal in Scotland; Fig.(1.5a)

Solitons have been known as a special kind of "solitary waves" that
formed in any medium where nonlinearity and dispersion are balanced.

Furthermore, they have an elastic scattering property, and retain their

shapes and speeds after colliding with each other; Fig.(1.5b)

Solitons become the solutions of classes of nonlinear weakly dispersive
partial differential equations in many physical systems (such as K-dV, KP

equations etc.).

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