On uniqueness properties of solutions of the k-generalized KdV equations

By Luis Escauriaza, Carlos E. Kenig, Gustavo Ponce, Luis Vega. 2006

107 citations recorded by the source corpus.

In this paper we study uniqueness properties of solutions of the so-called k-generalized Korteweg–de Vries equations. Our goal is to obtain sufficient conditions on the behavior of the difference u1−u2 of two solutions u1,u2 of (1.1) at two different times t0=0 and t1=1 which guarantee that u1≡u2.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1d82db089bab10f67d7fcb63b8c6bb7ba74f7180

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Lorenzo Brandolese
2. Germán E. Fonseca
3. Gustavo Ponce
4. Bingyu Zhang
5. Lionel Rosier
6. Felipe Linares
7. Marco Cannone
8. Olivier Glass

In Mathematical Physics

1. Bingyu Zhang
2. Lionel Rosier
3. Lorenzo Brandolese
4. Germán E. Fonseca
5. Gustavo Ponce
6. Felipe Linares
7. Olivier Glass
8. Marco Cannone

In Statistical and Nonlinear Physics

1. Lionel Rosier
2. Lorenzo Brandolese
3. Bingyu Zhang
4. Germán E. Fonseca
5. Gustavo Ponce
6. Carlos E. Kenig
7. A. Alexandrou Himonas

Citations in the corpus

• Existence of Solitary Waves and Periodic Waves to a Perturbed Generalized KdV Equation (2014, unknown): “Recently, many researchers have paid attention to the perturbed and generalized KdV equation, for example, [3, 4, 5, 7, 10, 13, 14,15,16,17,18,19].”
• The IVP for the Benjamin-Ono equation in weighted Sobolev spaces (2010, background): “We recall that unique continuation principles for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation have been established in [9] and [10] resp.”
• Breakdown for the Camassa-Holm Equation Using Decay Criteria and Persistence in Weighted Spaces (2012, methodology): “A second motivation of such analysis is provided by the paper of Himonas, Misio lek, Ponce and Zhou [20], and by the earlier work of Escauriaza, Kenig, Ponce and Vega, [13], [14] on the unique continuation of solutions to nonlinear dispersive equations (the Schrödinger and the generalized k-general”
• Control of a Korteweg-de Vries equation: A tutorial (2013, unknown): “See also [51, 21, 25].”
• Unique continuation property and control for the Benjamin–Bona–Mahony equation on a periodic domain (2013, methodology): “The UCP for KdV was established in [47] by the inverse scattering approach, in [11,39,45] by means of Carleman estimates, and in [4] by a perturbative approach and Fourier analysis.”