Lump solutions and interaction solutions for <inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></math></inline-formula>-dimensional KPI equation

Yanfeng GUO; Zhengde DAI; Chunxiao GUO

doi:10.1007/s11464-021-0973-y

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Front. Math. China ›› 2022, Vol. 17 ›› Issue (5) : 875-886. DOI: 10.1007/s11464-021-0973-y

RESEARCH ARTICLE

Lump solutions and interaction solutions for $(2 + 1)$ -dimensional KPI equation

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Abstract

The lump solutions and interaction solutions are mainly investigated for the $(2 + 1)$ -dimensional KPI equation. According to relations of the undetermined parameters of the test functions, the N-soliton solutions are showed by computations of the Maple using the Hirota bilinear form for $(2 + 1)$ -dimensional KPI equation. One type of the lump solutions for $(2 + 1)$ -dimensional KPI equation has been deduced by the limit method of the N-soliton solutions. In addition, the interaction solutions between the lump and N-soliton solutions of it are studied by the undetermined interaction functions. The sufficient conditions for the existence of the interaction solutions are obtained. Furthermore, the new breather solutions for the $(2 + 1)$ -dimensional KPI equation are considered by the homoclinic test method via new test functions including more parameters than common test functions.

Keywords

Lump solutions / $(2 + 1)$ -dimensional KPI equation / interaction solutions / N-soliton solutions / breather solutions

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Yanfeng GUO, Zhengde DAI, Chunxiao GUO. Lump solutions and interaction solutions for

(2 + 1)

-dimensional KPI equation. Front. Math. China, 2022, 17(5): 875‒886 https://doi.org/10.1007/s11464-021-0973-y

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