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2021•Research SquareOpen access

Two new Painlev´e integrable KdV–Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and new negative-order KdV-CBS equation

Abdul‐Majid Wazwaz

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Abstract

Abstract In this work, we develop two new (3+1)-dimensional KdV–Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and (3+1)-dimensional negative-order KdV-CBS (nKdV-nCBS) equation. The newly developed equations pass the Painlev´e integrability test via examining the compatibility conditions for each developed model. We examine the dispersion relation and derive multiple soliton solutions for each new equation.

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Abstract In this work, we develop two new (3+1)-dimensional KdV–Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and (3+1)-dimensional negative-order KdV-CBS (nKdV-nCBS) equation. The newly developed equations pass the Painlev´e integrability test via examining the compatibility conditions for each developed model. We examine the dispersion relation and derive multiple soliton solutions for each new equation.

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Available abstract

Abstract In this work, we develop two new (3+1)-dimensional KdV–Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and (3+1)-dimensional negative-order KdV-CBS (nKdV-nCBS) equation. The newly developed equations pass the Painlev´e integrability test via examining the compatibility conditions for each developed model. We examine the dispersion relation and derive multiple soliton solutions for each new equation.

Key concepts: Korteweg–de Vries equation, Integrable system, Mathematics, Mathematical physics, Physics, Nonlinear system, Quantum mechanics

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Two new Painlev´e integrable KdV–Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and new negative-order KdV-CBS equation — Research Paper | ScholarLens