Abundant exact closed-form solutions and solitonic structures for the double-chain deoxyribonucleic acid (DNA) model

Kumar, Sachin; Kumar, Amit; Kharbanda, Harsha

doi:10.1007/s13538-021-00913-8

Cited by 42 publications

(6 citation statements)

References 31 publications

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“…As we all know, many problems in natural science can be expressed by the nonlinear partial differential equations (NPDEs), such as the heat conduction, chemical reaction, physics, soil moisture, hydrodynamics, vibration, nonlinear circuits and nonlinear optics, etc [1][2][3][4][5][6][7][8][9][10][11][12]. Considering the diversity of the NPDEs and the complexity of nonlinear problems, there is currently no method to obtain various solutions for all NPDEs.…”

Section: Introductionmentioning

confidence: 99%

Soliton molecules, Y-type soliton and complex multiple soliton solutions to the extended (3+1)-dimensional Jimbo-Miwa equation

Wang

2024

Phys. Scr.

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The central purpose of this paper is extracting some novel and interesting soliton solutions of the extended (3+1)-dimensional Jimbo-Miwa equation(JME) which acts as an extension of the classic (3+1)-dimensional JME for the plasma and optics. First, we study the N-soltion solutions that is developed by the Hirota bilinear method (HBM). Then, the soliton molecules and Y-type soliton solutions are constructed via imposing the novel resonance conditions to the N-soltion solutions. In addition, we also explore the complex multiple soliton solutions via the HBM. The dynamic properties of the N-soltion, soliton molecules, Y-type soliton as well as the complex multiple soliton solutions are presented graphically. The developed soliton solutions of this research are all new and can enable us apprehend the nonlinear dynamic behaviors of the extended (3+1)-dimensional JME better.

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Section: Introductionmentioning

confidence: 99%

Soliton molecules, Y-type soliton and complex multiple soliton solutions to the extended (3+1)-dimensional Jimbo-Miwa equation

Wang

2024

Phys. Scr.

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“…Among them, soliton theory has made significant breakthroughs and progress since the 1960s. It not only opens up research fields in interdisciplinary fields such as mathematics and physics, but also is widely used in plasma, condensed matter physics, optics, biology, communication engineering, etc [1][2][3][4][5][6][7][8]. In nature, many nonlinear phenomena can ultimately be represented by the NEEs.…”

Section: Introductionmentioning

confidence: 99%

Resonant Y-type soliton, X-type soliton and some novel hybrid interaction solutions to the (3+1)-dimensional nonlinear evolution equation for shallow-water waves

Wang

2024

Phys. Scr.

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This research aims to explore some novel solutions to the (3+1)-dimensional nonlinear evolution equation (NEE) for the shallow-water waves. The resonant Y-type soliton (YTS) and X-type soliton (XTS) solutions are derived by applying the novel resonant conditions on the N-soliton solutions(N-SSs) which are extracted via the Hirota bilinear approach. Additionally, some novel and interesting hybrid interaction solutions like the interaction between Y-type soliton and 1-soliton, interaction between Y-type soliton and 1-breather solution, interaction between the Y-type soliton and the soliton molecule on the (x,y)-plane, and interaction between the X-type soliton and 1-soliton are also ascertained. The dynamic attributes of the obtained solutions are described graphically to unveil their physical behaviors. The findings in this work can help us better apprehend the nonlinear dynamics of the considered equation.

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“…Nonlinear science is an important tool in modern mathematics, occupying an important position in science and effectively solving the most complex phenomena in nature. The nonlinear partial differential equations (NPDEs) have wide applications in various fields such as plasma physics [1,2], optics [3][4][5][6], thermodynamics [7,8], vibration [9,10], biology [11,12], and other fields. Soliton theory is an important part of nonlinear scientific content, and finding efficacious approaches to develop soliton solutions is the hot spot for scholars.…”

Section: Introductionmentioning

confidence: 99%

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

Wang,

Shi,

et al. 2024

Math Methods in App Sciences

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This research mainly concerned with some new solutions of the (3 + 1)‐dimensional nonlinear evolution equation (NEE). First, we extract the resonant multiple soliton solutions (RMSSs) by taking advantage of the linear superposition principle (LSP) and weight algorithm (WA). Then the non‐singular complexiton and singular complexiton solutions are developed by introducing pairs of the conjugate parameters. Besides, the complex multiple‐soliton solutions are also explored with the aid of the bilinear approach. The graph descriptions of the attained solutions are paraded to show the dynamical properties. The outcomes of this work are all new and are desirous to bring some new perspective to the investigation of the complexiton solutions to the other partial differential equations (PDEs).

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Abundant exact closed-form solutions and solitonic structures for the double-chain deoxyribonucleic acid (DNA) model

Cited by 42 publications

References 31 publications

Soliton molecules, Y-type soliton and complex multiple soliton solutions to the extended (3+1)-dimensional Jimbo-Miwa equation

Soliton molecules, Y-type soliton and complex multiple soliton solutions to the extended (3+1)-dimensional Jimbo-Miwa equation

Resonant Y-type soliton, X-type soliton and some novel hybrid interaction solutions to the (3+1)-dimensional nonlinear evolution equation for shallow-water waves

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

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