Optimal Subalgebra of GKP by Using Killing Form, Conservation Law and Some More Solutions

Kumar, Raj; Kumar, Avneesh

doi:10.1007/s40819-021-01211-2

Cited by 4 publications

(2 citation statements)

References 33 publications

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“…Lies theory reduces the number of independent variables in the system by one. For applications of the method, one can refer to some articles [24][25][26][27][28][29]. We obtained a more variety of solutions of CKOEs (1) than previously reported results in [9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 80%

Some invariant solutions of coupled Konno-Oono equations arising in electromagnetic and quantum fields

Kumar¹,

Kumar²

2022

Phys. Scr.

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The goal of this study is to construct a novel family of travelling wave solutions for the system of (1 + 1)-coupled Konno-Oono equations (CKOEs). It occurs in optical nonlinear media, electromagnetic fields, plasma physics, and quantum fields. The invariant property of Lie symmetry analysis is exploited to extract analytical solutions. Lie symmetry analysis provides new similarity solutions for the system. A new variety of eighteen analytical solutions are compared to the reported results and the authors’ recently published work. In the previous results, a specific form of CKOEs with only two components, u and v, was solved in almost all cases, whereas in this study, a family of solutions was attained for three variables, u, v, and w. Solution profiles are portrayed via numerical simulation in order to make the solutions physically relevant.

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Section: Introductionmentioning

confidence: 80%

Some invariant solutions of coupled Konno-Oono equations arising in electromagnetic and quantum fields

Kumar¹,

Kumar²

2022

Phys. Scr.

Self Cite

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“…To study the application of Lie-symmetry theory and STM, some research articles [29][30][31][32][33][34] are also relevant.…”

Section: Infinitesimal Generators Via Classical Lie-symmetrymentioning

confidence: 99%

Some more variety of analytical solutions to (2+1)-Bogoyavlensky-Konopelchenko equation

Kumar,

Pandey,

Yadav

et al. 2024

Phys. Scr.

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The goal of this study is to get analytical solutions to the Bogoyavlensky-Konopelchenko equation, which describes an interaction of a long-wavelength wave moving along the x-axis and a Riemann wave-form moving along the y-axis. The equation has been widely used in soliton theory, fluid dynamics, optics, biological systems, and differential geometry. It is a member of the Ablowitz-Kaup-Newell-Segur hierarchy of integrable systems. By exploiting the classical Lie symmetry approach, the equation is reduced to an ordinary differential equation. After solving the second similarity reduction, the authors derived a novel class of solutions for each case. Additionally, the derived solutions comprise some parameters, and various functions might be utilized to explore wave profiles like stationary, dark, and bright soliton, parabolic dark and bright soliton, and progressive nature. Solutions are compared with previous researches [18-25] to show novelty of results. Solutions can help with numerous applications in physics, such as fluid dynamics, plasma physics, and nonlinear optics.

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Dynamics of One-Dimensional Motion of a Gas Under the Influence of Monochromatic Radiation

Tanwar

Sahu²

2023

Qual. Theory Dyn. Syst.

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Optimal Subalgebra of GKP by Using Killing Form, Conservation Law and Some More Solutions

Cited by 4 publications

References 33 publications

Some invariant solutions of coupled Konno-Oono equations arising in electromagnetic and quantum fields

Some invariant solutions of coupled Konno-Oono equations arising in electromagnetic and quantum fields

Some more variety of analytical solutions to (2+1)-Bogoyavlensky-Konopelchenko equation

Dynamics of One-Dimensional Motion of a Gas Under the Influence of Monochromatic Radiation

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