Breather’s Properties within the Framework of the Modified Korteweg–de Vries Equation
Abstract
:1. Introduction
2. MKdV-Breather
- q << p: and as in the linear problem;
- q >> p: and as in the two-soliton solution;
- q = p, and as in the intermediate case.
3. Breather’s Extrema
- (i)
- case: q/p >> 1. Let us fix q = 1, p = 0.2 ().
- (ii)
- case: q/p << 1. Let us fix q = 0.2, p = 1 ().
- (iii)
- case: q/p = 1. Let us fix q = 1, p = 1 ().
4. Breather’s Invariants
5. Breather’s Moments
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Didenkulova, E.; Pelinovsky, E. Breather’s Properties within the Framework of the Modified Korteweg–de Vries Equation. Symmetry 2020, 12, 638. https://doi.org/10.3390/sym12040638
Didenkulova E, Pelinovsky E. Breather’s Properties within the Framework of the Modified Korteweg–de Vries Equation. Symmetry. 2020; 12(4):638. https://doi.org/10.3390/sym12040638
Chicago/Turabian StyleDidenkulova, Ekaterina, and Efim Pelinovsky. 2020. "Breather’s Properties within the Framework of the Modified Korteweg–de Vries Equation" Symmetry 12, no. 4: 638. https://doi.org/10.3390/sym12040638
APA StyleDidenkulova, E., & Pelinovsky, E. (2020). Breather’s Properties within the Framework of the Modified Korteweg–de Vries Equation. Symmetry, 12(4), 638. https://doi.org/10.3390/sym12040638