On non-autonomous differential-difference AKP, BKP and CKP equations.

Area of Science:

• Mathematical Physics
• Nonlinear Dynamics
• Integrable Systems

Background:

• The direct linearization framework provides a powerful method for analyzing discrete integrable systems.
• Kadomtsev-Petviashvili (KP)-type equations are fundamental in studying nonlinear wave phenomena.

Purpose of the Study:

• To establish novel non-autonomous differential-difference equations based on the direct linearization of discrete KP-type equations.
• To explore integrable properties and potential applications of these new models.

Main Methods:

• Direct linearization framework applied to discrete Kadomtsev-Petviashvili-type equations.
• Construction of six new non-autonomous differential-difference equations across AKP, BKP, and CKP classes.

Main Results:

• Successfully derived three AKP, two BKP, and one CKP non-autonomous differential-difference equations.
• Two models, one BKP and one CKP, are in (2+2)-dimensional form.
• All derived equations exhibit integrability, ensuring soliton-type solutions and multi-dimensional consistency.

Conclusions:

• The direct linearization method effectively generates new integrable non-autonomous differential-difference equations.
• These novel equations extend the family of integrable systems and offer new avenues for studying nonlinear phenomena.