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Spring–mass behavior of solitons under the influence of an external force field within the modified Korteweg–de Vries equation
Chaos, Solitons and Fractals. 2025. Vol. 196. Article 116422.
We investigate the interaction of solitons with an external periodic field within the framework of the modified Korteweg–de Vries (mKdV) equation. In the case of small perturbation a simple dynamical system is used to
describe the soliton behavior. Equilibrium points of this dynamical system are computed when the external
force travels at a constant speed. Assuming that the external force moves with sinusoidal speed, we demonstrate
that the soliton behavior is qualitatively similar to the constant-speed case. Besides, a resonant frequency is
derived from the asymptotic theory without using the classical broad force approximation. The results obtained
from the dynamical system are compared with fully nonlinear direct numerical simulations, which reveal that
the soliton solution exhibits spiral-like behavior in the soliton amplitude versus soliton phase space. Moreover,
when the external force oscillates at the resonant frequency, the trajectories in the soliton phase versus soliton
amplitude exhibit chaotic behavior.
Keywords: asymptoticsнелинейные волнысолитоныsolitonsnonlinear wavesасимптотикиtrapped wavesзахваченные волны
Publication based on the results of:
D.V. Khomitsky, Lavrukhina E. A., Krasavin D. P. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 22 Article 225414
We study coherent electric manipulation of magnetic field induced localized states at a double kink of a helical edge in a HgTe/CdHgTe quantum well. An in-plane magnetic field opens a gap in the one-dimensional (1D) edge spectrum, while changes in the edge orientation generate localized in-gap states at the kinks. We show that, for suitable ...
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Flamarion M. V., Pelinovsky E., Wave Motion 2027 Vol. 148 Article 103867
We consider the interaction of two solitary waves in the modified Benjamin–Bona–Mahony
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Budkov Y., Kalikin N., Journal of Chemical Physics 2026 Vol. 165 No. 16 Article 164108
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Lavrukhina E. A., Krasavin D. P., Krishtopenko S. S. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 22 Article 225414
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Vorontsova T., М.: Академия, 2025.
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Naumov A., Рубцов А. С., Samsonov S. et al., Успехи математических наук 2026 Т. 81 № 4 (490) С. 161–162
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We provide an infinite series of commutative finite-dimensional Gorenstein local algebras A_n for n ≥ 2. We give an elementary proof that the maximal ideal of every algebra A_n possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of A_n. The latter implies that the algebras A_n fail ...
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Gordin V. A., Efremenko D., Boundary-Layer Meteorology 2026 Vol. 192 No. 51
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Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
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Тукачев Н. В., Bataev V. А., Godunov I. А., Journal of Quantitative Spectroscopy and Radiative Transfer 2017 Vol. 192 P. 30–41
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Тукачев Н. В., Bataev V. A., Godunov I. A., Computational and Theoretical Chemistry 2017 Vol. 1113 P. 82–93
Equilibrium geometry parameters, harmonic vibrational frequencies and barriers to conformational transitions and conformer energy differences for N-methylacetamide (CH3CONHCH3) molecule in S0, S1 and T1 electronic states were calculated in MP2 (S0) and CASPT2 (S1, T1) levels of theory. It is known that there are two planar (or effectively planar) conformers of N-methylacetamide in the ground ...
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Burov N.A., Gaydukov R.K., Russian Journal of Mathematical Physics 2026 Vol. 33 No. 2 P. 263–275
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Schamel H., Pelinovsky E., Flamarion M. V., REVIEWS OF MODERN PLASMA PHYSICS 2026 Vol. 10 Article 3
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