Study of breathers, rogue waves and lump solutions for the nonlinear chains of atoms

Ahmed, Sarfaraz; Seadawy, Aly R.; Rizvi, Syed T. R.

doi:10.1007/s11082-022-03732-6

Cited by 29 publications

(7 citation statements)

References 56 publications

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“…Then and hence, Eq. ( 3 ) can be supposed as Foroutan et al 42 with the subsequent constants; here in this paper, we will find out wave solutions and conservation laws for nonlinear Eq. ( 6 ) with the use of an appropriate transformation method.…”

Section: Formation Of Modelmentioning

confidence: 97%

Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms

Junaid-U-Rehman

Kudra

Awrejcewicz

2023

Sci Rep

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Nonlinear chains of atoms (NCA) are complex systems with rich dynamics, that influence various scientific disciplines. The lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. We have converted assumed PDE into nonlinear ODE by using the optimal system. The new auxiliary scheme is used to find the Travelling wave solutions, while graphical behaviour visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, and fundamental principles in physics that assert certain quantities remain constant over time.

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Section: Formation Of Modelmentioning

confidence: 97%

Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms

Junaid-U-Rehman

Kudra

Awrejcewicz

2023

Sci Rep

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“…Optical solitons have been extensively applied in high-speed and high-capacity communication systems as an information carrier. The nonlinear Schrödinger Equation (NLSE) is one of the rarely used models in this context and describes the evolution in optics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Grey-Black Optical Solitons, Homoclinic Breather, Combined Solitons via Chupin Liu’s Theorem for Improved Perturbed NLSE with Dual-Power Law Nonlinearity

2023

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In this article, we consider the improved perturbed nonlinear Schrödinger Equation (IP-NLSE) with dual power law nonlinearity, which arises in optical fibers and photovoltaic-photo-refractive materials. We found grey and black optical solitons of the governing equation by means of a suitable complex envelope ansatz solution. By using the Chupin Liu’s theorem (CLT) for the grey and black solitons, we evaluated new categories of combined optical soliton (COS) solutions to the IP-NLSE. The propagation behaviors for homoclinic breathers (HB), multiwaves and M-shape solitons will be analytically examined. All new analytical solutions will be found by an ansatz function scheme and suitable transformations. Multiwave solitons have been reported by using a three-waves technique. Furthermore, two kinds of interactions for M-shape soliton through exponential functions will be examined.

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“…For instance, the Korteweg-de Vries equation governs shallow water wave dynamics near ocean shores and beaches, and the nonlinear Schrödinger's equation governs the propagation of solitons through optical fibers. Some examples of PDEs and their applications can be found in [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…where h 1 and h 1 are real constants. The cubic term in Equation (1) represents the nonlinear self-interaction in the high-frequency subsystem, which corresponds to a self-focusing effect in plasma physics.…”

Section: Introductionmentioning

confidence: 99%

Lump-Type Solutions, Lump Solutions, and Mixed Rogue Waves for Coupled Nonlinear Generalized Zakharov Equations

2023

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This article studies diverse forms of lump-type solutions for coupled nonlinear generalized Zakharov equations (CNL-GZEs) in plasma physics through an appropriate transformation approach and bilinear equations. By utilizing the positive quadratic assumption in the bilinear equation, the lump-type solutions are derived. Similarly, by employing a single exponential transformation in the bilinear equation, the lump one-soliton solutions are derived. Furthermore, by choosing the double exponential ansatz in the bilinear equation, the lump two-soliton solutions are found. Interaction behaviors are observed and we also establish a few new solutions in various dimensions (3D and contour). Furthermore, we compute rogue-wave solutions and lump periodic solutions by employing proper hyperbolic and trigonometric functions.

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Study of breathers, rogue waves and lump solutions for the nonlinear chains of atoms

Cited by 29 publications

References 56 publications

Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms

Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms

Grey-Black Optical Solitons, Homoclinic Breather, Combined Solitons via Chupin Liu’s Theorem for Improved Perturbed NLSE with Dual-Power Law Nonlinearity

Lump-Type Solutions, Lump Solutions, and Mixed Rogue Waves for Coupled Nonlinear Generalized Zakharov Equations

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