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of 129
pro vyhledávání: '"Ehrnström, Mats"'
We prove exact leading-order asymptotic behaviour at the origin for nontrivial solutions of two families of nonlocal equations. The equations investigated include those satisfied by the cusped highest steady waves for both the uni- and bidirectional
Externí odkaz:
http://arxiv.org/abs/2302.08856
Starting with the periodic waves earlier constructed for the gravity Whitham equation, we parameterise the solution curves through relative wave height, and use a limiting argument to obtain a full family of solitary waves. The resulting branch start
Externí odkaz:
http://arxiv.org/abs/2204.03274
We prove existence of small-amplitude modulated solitary waves for the full-dispersion Kadomtsev--Petviashvilii (FDKP) equation with weak surface tension. The resulting waves are small-order perturbations of scaled, translated and frequency-shifted s
Externí odkaz:
http://arxiv.org/abs/2110.03971
Autor:
Ehrnström, Mats, Wang, Yuexun
Publikováno v:
Discrete and Continuous Dynamical Systems-A, (2022)
We show that Whitham type equations u_t + u u_x -L u_x = 0, where L is a general Fourier multiplier operator of order \alpha \in [-1,1], \alpha\neq 0, allow for small solutions to be extended beyond their expected existence time. The result is valid
Externí odkaz:
http://arxiv.org/abs/2008.12722
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist large fami
Externí odkaz:
http://arxiv.org/abs/1907.07335
We study the bifurcation of periodic travelling waves of the capillary-gravity Whitham equation. This is a nonlinear pseudo-differential equation that combines the canonical shallow water nonlinearity with the exact (unidirectional) dispersion for fi
Externí odkaz:
http://arxiv.org/abs/1901.03534
Akademický článek
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Autor:
Ehrnström, Mats, Wang, Yuexun
Publikováno v:
SIAM J. Math. Anal.(2019)
We consider the fractional Korteweg-de Vries equation $u_t + u u_x - |D|^\alpha u_x = 0$ in the range of $-1<\alpha<1$ , $\alpha\neq0$. Using basic Fourier techniques in combination with the modified energy method we extend the existence time of clas
Externí odkaz:
http://arxiv.org/abs/1804.06297
Autor:
Ehrnström, Mats, Groves, Mark
The KP-I equation \[ (u_t-2uu_x+\tfrac{1}{2}(\beta-\tfrac{1}{3})u_{xxx})_x -u_{yy}=0 \] arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tension (Bond number $\beta>1/3$). This equation admits --- as an expl
Externí odkaz:
http://arxiv.org/abs/1802.04823
Autor:
Ehrnström, Mats, Pei, Long
Publikováno v:
Journal of Evolution Equations 2018
For both localized and periodic initial data, we prove local existence in classical energy space $H^s, s>\frac{3}{2}$, for a class of dispersive equations $u_{t}+(n(u))_{x}+Lu_{x}=0$ with nonlinearities of mild regularity. Our results are valid for s
Externí odkaz:
http://arxiv.org/abs/1709.04713