Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Darboux transformation

Sortuj według:

Ogranicz wyniki do:

Deformed solitons of a typical set of (2+1)-dimensional complex modified Korteweg–de Vries equations

Yuan Feng, Zhu Xiaoming, Wang Yulei

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 2

337--350

Deformed soliton solutions are studied in a typical set of (2+1)-dimensional complex modified Korteweg–de Vries (cmKdV) equations. Through constructing the determinant form of the n-fold Darboux transformation for these (2+1)-dimensional cmKdV equations, we obtain general order-n deformed soliton solutions using zero seeds. With no loss of generality, we focus on order-1 and order-2 deformed solitons. Three types of order-1 deformed solitons, namely, the polynomial type, the trigonometric type, and the hyperbolic type, are derived. Meanwhile, their dynamical behaviors, including amplitude, velocity, direction, periodicity, and symmetry, are also investigated in detail. In particular, the formulas of |q[1]| and trajectories are provided analytically, which are involved by an arbitrary smooth function f(y + 4λ2t). For order-2 cases, we obtain the general analytical expressions of deformed solitons. Two typical solitons, possessing different properties in temporal symmetry, are discussed.

Dressing of Zero-Range Potentials into Realistic Molecular Potentials of Finite Range

Leble S., Ponomarev D.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2010

Vol. 14, No 1-2

29-34

The zero-range potentials of the radial Schrodinger equation and their dressing are investigated. A sequence of Darboux transformations involving a set of parameters yields solvable potentials of a finite-range with physically meaningful properties. In particular, the newly obtained potential is matched to that resulting from the ab initio computation methods in terms of discrete and continuous spectrum parameters. The approach, being a companion to conventional quantum simulation methods, combines symbolical and numerical calculations and is expected to work best for molecules with high spherical symmetry, typically fullerenes.