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Area of Science:

Nonlinear optics
Condensed matter physics
Mathematical physics

Background:

Solitary waves are localized wave packets that maintain their shape during propagation.
Interfaces between different materials can support unique wave phenomena.
Nonlinear lattices, such as the Kronig-Penney type, exhibit complex wave behavior.

Purpose of the Study:

To develop a novel phase-space method for constructing analytical stationary solitary waves.
To investigate solitary waves at interfaces involving nonlinear lattices and homogeneous media.
To understand the conditions for the existence and characteristics of these localized solutions.

Main Methods:

A novel phase-space method is employed for the construction of analytical stationary solitary waves.
The method is applied to interfaces between Kronig-Penney type nonlinear lattices and linear/nonlinear homogeneous media.
It is also used for interfaces between two dissimilar nonlinear lattices.

Main Results:

Generic classes of localized solutions with zero or nonzero semi-infinite backgrounds are obtained.
Conditions for the existence of solutions with specific profile characteristics are provided, involving propagation constant, refractive index, and lattice dimensions.
The evolution of analytical solutions reveals remarkable robustness.

Conclusions:

The developed phase-space method offers physical insight into solitary wave profiles.
The identified conditions ensure the existence of specific solitary wave solutions.
The robustness of these analytical solutions suggests potential for experimental observation.