Dynamical Study of Newly Created Analytical Solutions, Bifurcation Analysis, and Chaotic Nature of the Complex Kraenkel-Manna-Merle System

被引:13
作者
Rani, Setu [1 ]
Kumar, Sachin [2 ]
Kumar, Raj [3 ]
机构
[1] Univ Delhi, Dept Math, Lady Shri Ram Coll Women, Delhi 110024, India
[2] Univ Delhi, Fac Math Sci, Dept Math, Delhi 110007, India
[3] Univ Delhi, Kirori Mal Coll, Dept Math, Delhi 110007, India
关键词
Analytical methods; Nonlinear evolution equation; Extended sinh-Gordon equation expansion method; Modified auxiliary equation method; Bifurcation analysis; NONLINEAR SCHRODINGER-EQUATION; STABILITY ANALYSIS; OPTICAL SOLITONS; WAVE SOLUTIONS;
D O I
10.1007/s12346-024-01148-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The present research explores the analytical solutions and dynamics of complex Kraenkel-Manna-Merle system, which are exploited in ceramic-like materials with magnetic characteristics in electronics. Two distinct approaches, the extended sinh-Gordon equation expansion and the modified auxiliary equation are employed to derive soliton solutions in various function forms, including hyperbolic, trigonometric, rational, and Jacobi elliptic functions. The stability and accuracy of these solutions are confirmed through modulation instability analysis. Several specific solutions are illustrated through numerical simulations after assigning values to the free parameters. By back-substituting into the original model, the newly generated solutions confirm the validity of the new findings and ensure their accuracy. The obtained multiple soliton solutions show that the two approaches are effective, efficient, reliable, and potent for studying nonlinear evolution equations. Furthermore, a transformation converted the system into a planar dynamical system, allowing phase portraits to be analyzed. Moreover, the introduction of a perturbed term uncovered chaotic behavior across a range of parameter values, illustrated through both two-dimensional and three-dimensional graphics. The study presents novel analytical solutions that offer insights into nonlinear short wave interactions, which have not been previously documented using these methodologies.
引用
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页数:28
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共 49 条
[1]   Effects of the higher-order dispersion on solitary waves and modulation instability in a monomode fiber [J].
Akinyemi L. ;
Houwe A. ;
Abbagari S. ;
Wazwaz A.-M. ;
Alshehri H.M. ;
Osman M.S. .
Optik, 2023, 288
[2]   A novel approach to study generalized coupled cubic Schrödinger-Korteweg-de Vries equations [J].
Akinyemi, Lanre ;
Veeresha, P. ;
Darvishi, M. T. ;
Rezazadeh, Hadi ;
Senol, Mehmet ;
Akpan, Udoh .
JOURNAL OF OCEAN ENGINEERING AND SCIENCE, 2024, 9 (01) :13-24
[4]   Soliton solutions of the generalized Davey-Stewartson equation with full nonlinearities via three integrating schemes [J].
Arshed, Saima ;
Raza, Nauman ;
Alansari, Monairah .
AIN SHAMS ENGINEERING JOURNAL, 2021, 12 (03) :3091-3098
[5]   Analyzing specific waves and various dynamics of multi-peakons in (3+1)-dimensional p-type equation using a newly created methodology [J].
Dhiman, Shubham Kumar ;
Kumar, Sachin .
NONLINEAR DYNAMICS, 2024, 112 (12) :10277-10290
[6]   Bifurcation and chaotic patterns of the chirped solitary waves in nonlinear electrical transmission line lattice (vol 186, 115231, 2024) [J].
Houwe, Alphonse ;
Abbagari, Souleymanou ;
Akinyemi, Lanre ;
Doka, Serge Yamigno ;
Metwally, Ahmed Sayed M. ;
Ahmad, Hijaz .
CHAOS SOLITONS & FRACTALS, 2024, 186
[7]   Qualitative behavior and variant soliton profiles of the generalized P-type equation with its sensitivity visualization [J].
Jhangeer, Adil ;
Raza, Nauman ;
Ejaz, Ayesha ;
Rafiq, Muhammad Hamza ;
Baleanu, Dumitru .
ALEXANDRIA ENGINEERING JOURNAL, 2024, 104 :292-305
[8]   A study of travelling, periodic, quasiperiodic and chaotic structures of perturbed Fokas-Lenells model [J].
Jhangeer, Adil ;
Rezazadeh, Hadi ;
Seadawy, Aly .
PRAMANA-JOURNAL OF PHYSICS, 2021, 95 (01)
[9]   Polarized waveguide excitations in microwave ferrites: The singularity structure analysis [J].
Kamdem, Brice A. ;
Lemoula, Romuald K. K. ;
Kuetche, Victor K. ;
Defo, Jean J. ;
Noule, Raissa S. ;
Youssoufa, Saliou .
PHYSICA SCRIPTA, 2021, 96 (11)
[10]   Exact solutions and conservation laws of the fourth-order nonlinear Schrödinger equation for the embedded solitons [J].
Kudryashov N.A. ;
Nifontov D.R. .
Optik, 2024, 303