Superposed hyperbolic kink and pulse solutions of coupled $φ$4, NLS and mKdV equations (Journal Article) (2024)

Journal Article · Thu Jul 14 00:00:00 EDT 2022 · International Journal of Modern Physics B

DOI:https://doi.org/10.1142/s0217979222501429· OSTI ID:2342052

Khare, Avinash[1]; Saxena, Avadh ^[2]

Search OSTI.GOV for author "Saxena, Avadh"
Search OSTI.GOV for ORCID "0000-0002-3374-3236"
View ORCID profile

Savitribai Phule Pune Univ. (India)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

+ Show Author Affiliations

Here, in this paper, we obtain novel solutions of a coupled $$φ$$⁴, a coupled nonlinear Schrödinger equation and a coupled modified Korteweg de Vries equation which can be re-expressed as a linear superposition of either the sum or the difference of two hyperbolic pulse solutions or the sum of either a two-kink or a kink and an antikink solution. These results demonstrate that the notion of superposed solutions extends to coupled nonlinear equations as well.

View Accepted Manuscript (DOE)

Cite

Export

Save

References (26)

Successive phase transitions and kink solutions in $ϕ^{8}$ , $ϕ^{10}$ , and $ϕ^{12}$ field theories Khare, Avinash; Christov, Ivan C.; Saxena, Avadh Physical Review E, Vol. 90, Issue 2 https://doi.org/10.1103/PhysRevE.90.023208	journal	August 2014
Soliton structures in $P {(φ)}_{2}$ Lohe, M. A. Physical Review D, Vol. 20, Issue 12 https://doi.org/10.1103/PhysRevD.20.3120	journal	December 1979
Forces between kinks and antikinks with long-range tails Manton, N. S. Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 6 https://doi.org/10.1088/1751-8121/aaf9d1	journal	January 2019
Family of potentials with power law kink tails Khare, Avinash; Saxena, Avadh Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 36 https://doi.org/10.1088/1751-8121/ab30fd	journal	August 2019
Kink-antikink collisions and multi-bounce resonance windows in higher-order field theories Christov, Ivan C.; Decker, Robert J.; Demirkaya, A. Communications in Nonlinear Science and Numerical Simulation, Vol. 97 https://doi.org/10.1016/j.cnsns.2021.105748	journal	June 2021
Topological defects with power-law tails Radomskiy, R. V.; Mrozovskaya, E. V.; Gani, V. A. Journal of Physics: Conference Series, Vol. 798 https://doi.org/10.1088/1742-6596/798/1/012087	journal	January 2017
Scattering of the φ8 kinks with power-law asymptotics Belendryasova, Ekaterina; Gani, Vakhid A. Communications in Nonlinear Science and Numerical Simulation, Vol. 67 https://doi.org/10.1016/j.cnsns.2018.07.030	journal	February 2019
Wide class of logarithmic potentials with power-tower kink tails Khare, Avinash; Saxena, Avadh Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 31 https://doi.org/10.1088/1751-8121/ab84ac	journal	July 2020
Logarithmic potential with super-super-exponential kink profiles and tails Khare, Avinash; Saxena, Avadh Physica Scripta, Vol. 95, Issue 7 https://doi.org/10.1088/1402-4896/ab8eeb	journal	May 2020
Solitons of Coupled Scalar Field Theories in Two Dimensions Rajaraman, R. Physical Review Letters, Vol. 42, Issue 4 https://doi.org/10.1103/PhysRevLett.42.200	journal	January 1979
Composite-kink solutions of coupled nonlinear wave equations Katsura, Hosho Physical Review D, Vol. 89, Issue 8 https://doi.org/10.1103/PhysRevD.89.085019	journal	April 2014
Domain walls carrying a U(1) charge Lensky, V. A.; Gani, V. A.; Kudryavtsev, A. E. Journal of Experimental and Theoretical Physics, Vol. 93, Issue 4 https://doi.org/10.1134/1.1420436	journal	October 2001
Kinklike structures in scalar field theories: From one-field to two-field models Bazeia, D.; Losano, L.; Santos, J. R. L. Physics Letters A, Vol. 377, Issue 25-27 https://doi.org/10.1016/j.physleta.2013.04.047	journal	October 2013
Orbit-based deformation procedure for two-field models Afonso, V. I.; Bazeia, D.; Leon, M. A. Gonzalez Physical Review D, Vol. 76, Issue 2 https://doi.org/10.1103/PhysRevD.76.025010	journal	July 2007
Extended solutions via the trial orbit method for two-field models Gomes, A. R.; Bazeia, D. Physica Scripta, Vol. 79, Issue 5 https://doi.org/10.1088/0031-8949/79/05/055005	journal	April 2009
Breathers and compound solitons in the system of acoustic phonons Smagin, V. V.; Tankeyev, A. P.; Borich, M. A. The Physics of Metals and Metallography, Vol. 108, Issue 5 https://doi.org/10.1134/S0031918X09110015	journal	November 2009
Semiclassical bound states in an asymptotically free theory Dashen, Roger F.; Hasslacher, Brosl; Neveu, André Physical Review D, Vol. 12, Issue 8 https://doi.org/10.1103/PhysRevD.12.2443	journal	October 1975
Soliton excitations in polyacetylene and relativistic field theory models Campbell, D. K.; Bishop, A. R. Nuclear Physics B, Vol. 200, Issue 2 https://doi.org/10.1016/0550-3213(82)90089-X	journal	February 1982
Multipolaron solutions of the Gross-Neveu field theory: Toda potential and doped polymers Saxena, Avadh; Bishop, A. R. Physical Review A, Vol. 44, Issue 4 https://doi.org/10.1103/PhysRevA.44.R2251	journal	August 1991
Full phase diagram of the massive Gross–Neveu model Schnetz, Oliver; Thies, Michael; Urlichs, Konrad Annals of Physics, Vol. 321, Issue 11 https://doi.org/10.1016/j.aop.2005.12.007	journal	November 2006
Classical motion in coupled double well potentials: trajectories, poincare plots, liapunov exponents, and chaos Abel, Thomas; Siems, Rolf Ferroelectrics, Vol. 153, Issue 1 https://doi.org/10.1080/00150199408016563	journal	March 1994
Magnetic phases of rare-earth hexagonal manganites Curnoe, S. H.; Munawar, I. Physica B: Condensed Matter, Vol. 378-380 https://doi.org/10.1016/j.physb.2006.01.249	journal	May 2006
Coupled Manakov equations in multimode fibers with strongly coupled groups of modes Mecozzi, Antonio; Antonelli, Cristian; Shtaif, Mark Optics Express, Vol. 20, Issue 21 https://doi.org/10.1364/OE.20.023436	journal	September 2012
Domain wall and periodic solutions of coupled ϕ4 models in an external field Khare, Avinash; Saxena, Avadh Journal of Mathematical Physics, Vol. 47, Issue 9 https://doi.org/10.1063/1.2345110	journal	September 2006
Soliton solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation Fan, Engui Physics Letters A, Vol. 282, Issue 1-2 https://doi.org/10.1016/S0375-9601(01)00161-X	journal	April 2001
Coupled KdV equations derived from two-layer fluids Lou, S. Y.; Tong, Bin; Hu, Heng-chun Journal of Physics A: Mathematical and General, Vol. 39, Issue 3 https://doi.org/10.1088/0305-4470/39/3/005	journal	December 2005

Similar Records

Superposed periodic kink and pulse solutions of coupled nonlinear equations

Journal Article · Thu Jul 27 00:00:00 EDT 2023 · Annals of Physics · OSTI ID:2342052

Khare, Avinash; Banerjee, Saikat; Saxena, Avadh Behari

Novel superposed kinklike and pulselike solutions for several nonlocal nonlinear equations

Journal Article · Fri Dec 16 00:00:00 EST 2022 · Journal of Mathematical Physics · OSTI ID:2342052

Khare, Avinash; Saxena, Avadh

New solutions of coupled nonlocal NLS and coupled nonlocal mKdV equations

Journal Article · Tue Feb 20 00:00:00 EST 2024 · Annals of Physics · OSTI ID:2342052

Khare, Avinash; Saxena, Avadh

Related Subjects

97 MATHEMATICS AND COMPUTING
Mathematics
superposed solutions
coupled nonlinear equations
solitons
kinks