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6 results on '"Ortenzi G"'

3. Nonlocal integrable PDEs from hierarchies of symmetry laws: The example of Pohlmeyer–Lund–Regge equation and its reflectionless potential solutions

Author

Demontis, F, Ortenzi, G, van der Mee, C, Demontis, F, Ortenzi, G, and van der Mee, C

Abstract

By following the ideas presented by Fukumoto and Miyajima in Fukumoto and Miyajima (1996) we derive a generalized method for constructing integrable nonlocal equations starting from any bi-Hamiltonian hierarchy supplied with a recursion operator. This construction provides the right framework for the application of the full machinery of the inverse scattering transform. We pay attention to the Pohlmeyer–Lund–Regge equation coming from the nonlinear Schrödinger hierarchy and construct the formula for the reflectionless potential solutions which are generalizations of multi-solitons. Some explicit examples are discussed

Published
2018

4. Nonlocal integrable PDEs from hierarchies of symmetry laws: The example of Pohlmeyer–Lund–Regge equation and its reflectionless potential solutions.

Author

Demontis, F., Ortenzi, G., and van der Mee, C.

Subjects
*MATHEMATICAL symmetry, *RECURSION theory, *INVERSE scattering transform, *SCHRODINGER equation, *NONLINEAR equations
Abstract

By following the ideas presented by Fukumoto and Miyajima in Fukumoto and Miyajima (1996) we derive a generalized method for constructing integrable nonlocal equations starting from any bi-Hamiltonian hierarchy supplied with a recursion operator. This construction provides the right framework for the application of the full machinery of the inverse scattering transform. We pay attention to the Pohlmeyer–Lund–Regge equation coming from the nonlinear Schrödinger hierarchy and construct the formula for the reflectionless potential solutions which are generalizations of multi-solitons. Some explicit examples are discussed. [ABSTRACT FROM AUTHOR]

Published
2018
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5. Exact solutions of the Hirota equation and vortex filaments motion

Author

Demontis, F, Ortenzi, G, Van Der Mee, C, ORTENZI, GIOVANNI, Van Der Mee, C., Demontis, F, Ortenzi, G, Van Der Mee, C, ORTENZI, GIOVANNI, and Van Der Mee, C.

Abstract

By using the Inverse Scattering Transform we construct an explicit soliton solution formula for the Hirota equation. The formula obtained allows one to get, as a particular case, the N-soliton solution, the breather solution and, most relevantly, a new class of solutions called multipole soliton solutions. We use these exact solutions to study the motion of a vortex filament in an incompressible Euler fluid with nonzero axial velocity.

Published
2015

6. Exact solutions of the Hirota equation and vortex filaments motion

Author

Francesco Demontis, Giovanni Ortenzi, C. van der Mee, Demontis, F, Ortenzi, G, and Van Der Mee, C

Subjects
Physics, Inverse scattering transform, Breather, Vortex filament, Motion (geometry), Statistical and Nonlinear Physics, Condensed Matter Physic, Condensed Matter Physics, MAT/07 - FISICA MATEMATICA, Soliton solution, Vortex, symbols.namesake, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Classical mechanics, Soliton solutions, Euler's formula, symbols, Compressibility, Soliton, Inverse Scattering Transform, Multipole expansion, Vortex filaments, Nonlinear Sciences::Pattern Formation and Solitons, Mathematical physics
Abstract

By using the Inverse Scattering Transform we construct an explicit soliton solution formula for the Hirota equation. The formula obtained allows one to get, as a particular case, the N -soliton solution, the breather solution and, most relevantly, a new class of solutions called multipole soliton solutions. We use these exact solutions to study the motion of a vortex filament in an incompressible Euler fluid with nonzero axial velocity.

Published
2015

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