TY - JOUR

T1 - The estimates of the ill-posedness index of the (deformed-) continuous Heisenberg spin equation

AU - Zhong, Penghong

AU - Chen, Ye

AU - Yang, Ganshan

N1 - Funding Information:
P.Z. was supported by the Tian Yuan Mathematical Foundation of China (Grant No. 11426068), the Project for Young Creative Talents of Ordinary University of Guangdong Province (Grant No. 2014KQNCX228), the Doctoral Start-up Fund of Natural Science Foundation of Guangdong Province (Grant No. 2014A030310330), the Research Award Fund for Outstanding Young Teachers in Guangdong Province (Grant No. Yq20145084601), the Special Innovation Projects of Universities in Guangdong Province (Grant No. 2018KTSCX161), and the Fund for Science and Technology of Guangzhou (Grant Nos. 201607010352 and 202102080428).
Publisher Copyright:
© 2021 Author(s).

PY - 2021/10/1

Y1 - 2021/10/1

N2 - Although the exact treatment of the continuous Heisenberg spin is already known, the exact solution of the deformed system is not found in the literature. In this paper, some traveling wave solutions of the deformed (indicated by the coefficient α) continuous Heisenberg spin equation are obtained. Based on the exact solution being constructed here, the ill-posedness results are proved by the estimation of the Fourier integral in Ḣs. If α = 0, the range of the mild ill-posedness index s is (1,32), which is consistent with the result of the formal analysis of the solution. Moreover, the upper bound of the strong ill-posedness index s jumps at α = 0: If α = 0, the upper bound is 2; if α = 0, then the upper bound jumps to 32.

AB - Although the exact treatment of the continuous Heisenberg spin is already known, the exact solution of the deformed system is not found in the literature. In this paper, some traveling wave solutions of the deformed (indicated by the coefficient α) continuous Heisenberg spin equation are obtained. Based on the exact solution being constructed here, the ill-posedness results are proved by the estimation of the Fourier integral in Ḣs. If α = 0, the range of the mild ill-posedness index s is (1,32), which is consistent with the result of the formal analysis of the solution. Moreover, the upper bound of the strong ill-posedness index s jumps at α = 0: If α = 0, the upper bound is 2; if α = 0, then the upper bound jumps to 32.

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U2 - 10.1063/5.0038377

DO - 10.1063/5.0038377

M3 - Article

AN - SCOPUS:85118242901

SN - 0022-2488

VL - 62

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 10

M1 - 101510

ER -