Conservation laws and line soliton solutions of a family of modified KP equations

Stephen C. Anco; Maria Luz Gandarias; Elena Recio

doi:10.3934/dcdss.2020225

Article Contents

2020, Volume 13, Issue 10: 2655-2665. Doi: 10.3934/dcdss.2020225

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Conservation laws and line soliton solutions of a family of modified KP equations

1.
Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S3A1, Canada
2.
Department of Mathematics, Faculty of Sciences, University of Cádiz, Puerto Real, Cádiz, 11510, Spain

Received: February 2019

Revised: July 2019

Early access: December 2019

Published: July 2020

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Abstract

A family of modified Kadomtsev-Petviashvili equations (mKP) in 2+1 dimensions is studied. This family includes the integrable mKP equation when the coefficients of the nonlinear terms and the transverse dispersion term satisfy an algebraic condition. The explicit line soliton solution and all conservation laws of low order are derived for all equations in the family and compared to their counterparts in the integrable case.

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Mathematics Subject Classification: 35C08, 37K05.

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Figure 1. Kinematically allowed region in $ (c,\theta) $ for the mKP family line soliton (40)

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Figure 2. Kinematically allowed region in $ (c,\theta) $ for the mKP family line soliton (40) in the defocussing case ($ \sigma_1 = -1 $)

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Figure 3. Profile of the mKP line soliton (39) and mKP family line soliton (40) and (45) for $ (h,w) = $ $ (1,1) $ (solid); $ (4,1) $ (long dash); $ (\tfrac{1}{5},1) $ (dash dot); $ (1,4) $ (dash); $ (1,\tfrac{1}{2}) $ (dot)

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Figure 4. Kinematically allowed region in $ (c,\theta) $ for the mKP family line soliton (45) in the defocussing case ($ \sigma_1 = -1 $)

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