Generalizations of the Camassa–Holm equation

By V. Novikov. 2009

566 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b7eac8a015a94a25739947152ccf62edc52801dc

How researchers see this paper

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

In Algebra and Number Theory

1. Yue Liu
2. Yongsheng Li
3. A. Alexandrou Himonas
4. Zhaoyang Yin
5. Peter J. Olver
6. John Holmes
7. Ying Fu
8. Shuanghu Zhang

In Geometry and Topology

1. Yue Liu
2. Changzheng Qu
3. Ying Fu
4. Shuanghu Zhang
5. Robin Ming Chen
6. John Holmes
7. Zhaoyang Yin
8. R. Thompson

In Statistical and Nonlinear Physics

1. Yue Liu
2. Changzheng Qu
3. Ying Fu
4. R. Thompson
5. Zhaoyang Yin
6. John Holmes
7. Robin Ming Chen
8. A. Alexandrou Himonas

Citations in the corpus

• Global weak solutions for the Novikov equation (2011, background): “It was discovered very recently by Novikov in a symmetry classification of nonlocal PDEs with cubic nonlinearity [24].”
• The Cauchy problem for the integrable Novikov equation (2012, background): “Introduction Recently, Vladimir Novikov [13] found a new integrable equation: ut − utxx + 4u(2)ux − 3uuxuxx − u(2)uxxx = 0.”
• Well-posedness, wave breaking and peakons for a modified μ-Camassa-Holm equation (2014, background): “7) have been studied respectively in [26,27,37,42,43].”
• The Cauchy problem for the Novikov equation (2012, background): “1) which was recently discovered by Vladimir Novikov in a symmetry classification of nonlocal PDEs with quadratic or cubic nonlinearity [14].”
• Analysis on the blow-up of solutions to a class of integrable peakon equations (2016, background): “In contrast to the DP equation, the Novikov equation [24] exhibits a cubic nonlinearity”
• A note on the Cauchy problem of the Novikov equation (2013, background): “It was discovered very recently by Novikov in a symmetry classification of nonlocal PDEs with cubic nonlinearity [2].”
• On the blow-up of solutions to the integrable modified Camassa–Holm equation (2014, methodology): “Two CH-type equations with cubic nonlinearities have been proposed: the modified CH equation (1.1) [13, 21], and the Novikov equation [20] mt + u 2mx + 3muux = 0, m = u− uxx.”
• Equations with Peakon Traveling Wave Solutions (2013, methodology): “In [20], Novikov investigated the question of integrability for Camassa–Holm type equations of the form (1− ∂2x)ut = P (u, ux, uxx, uxxx, . . .), (1.3) where P is a polynomial of u and its x-derivatives.”
• Well-posedness and global existence for the Novikov equation (2012, background): “It was discovered very recently by Novikov in a symmetry classification of nonlocal PDEs with cubic nonlinearity [21].”