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Asymptotic 𝐾-soliton-like solutions of the Zakharov-Kuznetsov type equations
Transactions of the American Mathematical Society ( IF 1.3 ) Pub Date : 2021-03-08 , DOI: 10.1090/tran/8331 Frédéric Valet
Transactions of the American Mathematical Society ( IF 1.3 ) Pub Date : 2021-03-08 , DOI: 10.1090/tran/8331 Frédéric Valet
Abstract:We study here the Zakharov-Kuznetsov equation in dimension 
, 
and 
and the modified Zakharov-Kuznetsov equation in dimension 
. Those equations admit solitons, characterized by their velocity and their shift. Given the parameters of 
solitons 
(with distinct velocities), we prove the existence and uniqueness of a multi-soliton 
such that 
The convergence takes place in 
with an exponential rate for all 
. The construction is made by successive approximations of the multi-soliton. We use classical arguments to control of 
-norms of the errors (inspired by Martel [Amer. J. Math. 127 (2005), pp. 1103-1140]), and introduce a new ingredient for the control of the 
-norm in dimension 
, by a technique close to monotonicity.
中文翻译：
Zakharov-Kuznetsov型方程的渐近𝐾-孤子解
摘要：我们在这里研究Zakharov-Kuznetsov方程的维，以及改进的Zakharov-Kuznetsov方程的维。这些方程式允许以速度和位移为特征的孤子。给定孤子的参数（具有不同的速度），我们证明多孤子的存在性和唯一性使得 所有的收敛都以指数速率进行。通过多孤子的逐次逼近来构造。我们使用经典参数来控制错误的-norm（受Martel启发[Amer。J. Math。127（2005），第1103-1140页]），并引入了控制-norm维度的新成分。，采用接近单调性的技术。
更新日期：2021-04-02
, and and the modified Zakharov-Kuznetsov equation in dimension . Those equations admit solitons, characterized by their velocity and their shift. Given the parameters of solitons (with distinct velocities), we prove the existence and uniqueness of a multi-soliton such that with an exponential rate for all . The construction is made by successive approximations of the multi-soliton. We use classical arguments to control of -norms of the errors (inspired by Martel [Amer. J. Math. 127 (2005), pp. 1103-1140]), and introduce a new ingredient for the control of the -norm in dimension , by a technique close to monotonicity. 中文翻译：
Zakharov-Kuznetsov型方程的渐近𝐾-孤子解
摘要：我们在这里研究Zakharov-Kuznetsov方程的维
，以及改进的Zakharov-Kuznetsov方程的维。这些方程式允许以速度和位移为特征的孤子。给定孤子的参数（具有不同的速度），我们证明多孤子的存在性和唯一性使得 以指数速率进行。通过多孤子的逐次逼近来构造。我们使用经典参数来控制错误的-norm（受Martel启发[Amer。J. Math。127（2005），第1103-1140页]），并引入了控制-norm维度的新成分。，采用接近单调性的技术。
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