Results 61 to 70 of about 178 (161)
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas
Symmetry, Integrability and Geometry: Methods and Applications, 2013 To every Darboux integrable system there is an associated Lie group G which is a fundamental invariant of the system and which we call the Vessiot group.
Mark E. Fels, Ian M. Anderson
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Journal of Mathematics, Volume 2026, Issue 1, 2026.In this work, we study the β‐fractional multicomponent Gross–Pitaevskii (G–P) system, which plays an important role in modeling Bose–Einstein condensates (BECs) and propagation in nonlinear waves. In Bose–Einstein condensation, the G–P equation is of great importance as it describes the condensate wave function’s behavior.
Naila Nasreen +5 more
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On Non-Point Invertible Transformations of Difference and Differential-Difference Equations
Symmetry, Integrability and Geometry: Methods and Applications, 2010 Non-point invertible transformations are completely described for difference equations on the quad-graph and for their differential-difference analogues. As an illustration, these transformations are used to construct new examples of integrable equations
Sergey Ya. Startsev
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Journal of Mathematics, Volume 2026, Issue 1, 2026.This study proposes a comprehensive study on fractional soliton solutions and chaotic nature for the temporal M‐fractional Yajima–Oikawa (YO) model in shortwave and longwave regimes. Utilizing the new Jacobian elliptic function method, the optical soliton solutions are examined with diverse categories, including kinky‐periodic wave, kink with bell wave,
Md. Mamunur Roshid +5 more
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Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
Symmetry, Integrability and Geometry: Methods and Applications, 2012 Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras $A_N$, $B_N$, $C_N$, $G_2$, $D_3$, $A_1^{(1)}$, $A_2^{(2)}$, $D^{(2)}_N$ these systems are proved to be ...
Rustem Garifullin +2 more
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Acta et Commentationes: Ştiinţe Exacte şi ale NaturiiIn this paper we find conditions for a singular point O(0, 0) of a center or a focus type to be a center, in a cubic differential system with one invariant straight line and one invariant cubic.
Dumitru Cozma
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Darboux integrability of the Lü system
Journal of Geometry and Physics, 2013 We characterize all the values of the parameters of the Lü system, for which it admits a Darboux first integral.
Jaume Llibre, Adam Mahdi, Clàudia Valls
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On integrable reductions of two-dimensional Toda-type lattices
Partial Differential Equations in Applied MathematicsThe article considers lattices of the two-dimensional Toda type, which can be interpreted as dressing chains for spatially two-dimensional generalizations of equations of the nonlinear Schrödinger type.
I.T. Habibullin, A.U. Sakieva
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Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations [PDF]
Journal of Sciences, Islamic Republic of Iran, 2006 We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i.
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On the Comparison of Darboux and Riemann Integrals in Constructive Analysis
Journal of Mathematical Sciences, 2014 7 ...
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