<p>By employing the Hirota’s bilinear and a novel limit method, the degenerate lump solutions containing anomalous scattering of lumps and weak interaction of multiple lumps are obtained to investigated the (2+1)-dimensional KP-BBM equation. The anomalous scattering of two lumps and also the asymptotic behavior of the anomalous scattering lumps are analyzed with more describing of the obtained solutions. Additionally, weak interactions of multiple lumps is also investigated. Moreover, the interaction between lump and scattering lumps is also found. This paper also presents an improved analytical method for solving the KP-BBM equation. The method involves transforming the equations into an ordinary differential equation and proposing a new form of solutions expressed as a polynomial with positive power. These rare degenerate lump solutions can enrich the understanding of lump properties. The novel conservation law theorem is investigated. The traveling wave solutions to mentioned model using the improved <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\tan (\phi /2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>tan</mo> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">/</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-expansion approach are explored. Stability properties to three type of solutions including periodic, soliton and kink solutions are analyzed and these solutions have been proven to be stable. The modulation instability analysis along with analysis of graphs is arrived. The proposed strategies are reliable and effective. The nonlinear KP-BBM admits a wide variety of innovative solutions. To illustrate the physical structure and attributes of the obtained solitons, this study depicts density plots along with three- and two-dimensional graphs. The visual representations of some of the solutions in the figures help to understand the physical characteristics of the numerous new soliton solutions and their corresponding behaviors. The results obtained imply that the concerned approach yield typical, effective, and compatible wave solutions and can be used for other nonlinear evolution equations. In short, the abstract can be stated as follows: <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\bullet $</EquationSource> <EquationSource Format="MATHML"><math> <mo>∙</mo> </math></EquationSource> </InlineEquation> The main objective is finding degenerate lump solutions and traveling solutions; <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\bullet $</EquationSource> <EquationSource Format="MATHML"><math> <mo>∙</mo> </math></EquationSource> </InlineEquation> The specific methods are Hirota bilinear method, conservation law, improved <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\tan (\phi /2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>tan</mo> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">/</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-expansion approach and modulation instability analysis; <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\bullet $</EquationSource> <EquationSource Format="MATHML"><math> <mo>∙</mo> </math></EquationSource> </InlineEquation> The novelty of the findings is investigating an important model with applicable methods where abundant solutions are achieved.</p>

Conservation Law, Stability Analysis, Degenerate Lump and Traveling Wave Solutions for (2+1)-Dimensional KP-BBM Equation

期刊论文
发表日期：

2025年11月3日

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Yuhong Xu,
Jalil Manafian,
Onur Alp Ilhan,
Arezu Aghazadeh,
A. A. Fattah,
K. H. Mahmoud,
Rawaa Abbas Barhe,
Wael Dheaa Kadhim

摘要

By employing the Hirota’s bilinear and a novel limit method, the degenerate lump solutions containing anomalous scattering of lumps and weak interaction of multiple lumps are obtained to investigated the (2+1)-dimensional KP-BBM equation. The anomalous scattering of two lumps and also the asymptotic behavior of the anomalous scattering lumps are analyzed with more describing of the obtained solutions. Additionally, weak interactions of multiple lumps is also investigated. Moreover, the interaction between lump and scattering lumps is also found. This paper also presents an improved analytical method for solving the KP-BBM equation. The method involves transforming the equations into an ordinary differential equation and proposing a new form of solutions expressed as a polynomial with positive power. These rare degenerate lump solutions can enrich the understanding of lump properties. The novel conservation law theorem is investigated. The traveling wave solutions to mentioned model using the improved $\tan (\phi /2)$ $tan (ϕ / 2)$ -expansion approach are explored. Stability properties to three type of solutions including periodic, soliton and kink solutions are analyzed and these solutions have been proven to be stable. The modulation instability analysis along with analysis of graphs is arrived. The proposed strategies are reliable and effective. The nonlinear KP-BBM admits a wide variety of innovative solutions. To illustrate the physical structure and attributes of the obtained solitons, this study depicts density plots along with three- and two-dimensional graphs. The visual representations of some of the solutions in the figures help to understand the physical characteristics of the numerous new soliton solutions and their corresponding behaviors. The results obtained imply that the concerned approach yield typical, effective, and compatible wave solutions and can be used for other nonlinear evolution equations. In short, the abstract can be stated as follows: $\bullet $ $∙$ The main objective is finding degenerate lump solutions and traveling solutions; $\bullet $ $∙$ The specific methods are Hirota bilinear method, conservation law, improved $\tan (\phi /2)$ $tan (ϕ / 2)$ -expansion approach and modulation instability analysis; $\bullet $ $∙$ The novelty of the findings is investigating an important model with applicable methods where abundant solutions are achieved.