Soliton solutions of generalized $$(3+1)$$ ( 3 + 1 ) -dime
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Soliton solutions of generalized (3 + 1)-dimensional Yu–Toda–Sasa–Fukuyama equation using Lie symmetry analysis Vishakha Jadaun1
· Nitin Raja Singh1
Received: 24 July 2020 / Revised: 15 August 2020 / Accepted: 18 August 2020 © Springer Nature Switzerland AG 2020
Abstract We analyze generalized (3 + 1)-dimensional Yu–Toda–Sasa–Fukuyama(YTSF) equation, a nonlinear evolution equation to understand pulse behavior when variations are strong. Using the Lie symmetry reduction, the generalized form of (3+1)-dimensional YTSF equation is reduced to ordinary differential equations. We introduce the main result for the analysis of soliton solutions that accounts for perturbation and dispersion of the waveform including linear and nonlinear effects. We discuss soliton interactions as a key feature of soliton based telecommunication transmission systems. Solitons propagate at distinct speed and interact quite strongly with each other having beaming correspondence. Though the interaction is transient, the coherence is diagonally placed. The solitons after perfectly elastic collisions recover their shape, amplitude and velocity except phase shift. Keywords Nonlinear dynamics · Nonlinear evolution equations · Generalized (3 + 1)-dimensional Yu–Toda–Sasa–Fukuyama equation · Lie group of transformations · Soliton · Soliton-based telecommunication technology
1 Introduction Nonlinear evolution equations (NLEEs) have been perused to explain diverse nonlinear phenomena ubiquitously present in scientific inquiry domain including its technological perspective. The scientific disciplines such as fluid dynamics, optics and solid state physics, astrophysics, cosmology, geology,oceanography,quantum mechanics, molecular biology , particle physics, among others utilize the potential of NLEEs [1–
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Vishakha Jadaun [email protected] Nitin Raja Singh [email protected]
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Department of Management studies, Indian Institute of Technology Delhi, New Delhi 110016, India 0123456789().: V,-vol
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V. Jadaun, N. R. Singh
7] with crucial results in integrable systems, nonlinear dynamics and supersymmetry. NLEEs are used to explain dispersion, dissipation, diffusion and convection processes. Research on solitary waves and solitons remains most vibrant area in mathematics and physics. A soliton is a solitary wave that arises from a delicate balance between nonlinear and dispersive effects. It maintains its shape while moving at the constant speed and its pulse width depends on the amplitude. For a non-dissipative system, a soliton is solitary wave whose amplitude, shape and velocity are conserved. A soliton collides with another soliton, their fundamental parameters remain conserved, except phase shift [8]. Envelope solitons emerges from the propagation of modulated phase waves in a dispersive nonlinear medium based on amplitude-dependent dispersion-relation. The term “Bright Soliton” refers to a soliton whose intensity is larger than the background, whereas “Dark Soliton” refers to a soliton whose intensity is smaller th
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