Ping Liu, Heng-Rui Xu, Jian-Rong Yang. The Boussinesq equation: Lax pair, Bäcklund transformation, symmetry group transformation and consistent Riccati expansion solvability [J]. Acta Physica Sinica, 2020, 69(1): 010203-1
- Acta Physica Sinica
- Vol. 69, Issue 1, 010203-1 (2020)
Fig. 1. The solution (49 ) with Formula (47 ). The free parameters are {n = 0.2, m = 0.5, a 1 = 1, a 3 = 1, k 1 = 1, k 2 = 1, ω 2 = 1, α = –0.8, β = 1}.
满足(47 )式的碰撞波解(49 )式. 自由参数为{n = 0.2, m = 0.5, a 1 = 1, a 3 = 1, k 1 = 1, k 2 = 1, ω 2 = 1, α = –0.8, β = 1}
Fig. 2. The solution (49 ) with Formula (47 ). The free parameters are {n = 0.2, m = 0.9, a 1 = 1, a 3 = 1, k 1 = 1, k 2 = 1, ω 2 = 1, α = –0.8, β = 1}.
满足(47 )式的碰撞波解(49 )式. 自由参数为 {n = 0.2, m = 0.9, a 1 = 1, a 3 = 1, k 1 = 1, k 2 = 1, ω 2 = 1, α = –0.8, β = 1}
Fig. 3. The density of u. The parameters of the Fig. (a) are the same as those of Figure 1 and the parameters of the Fig. (b) are the same as those of Figure 2 .
u 的密度函数图. 图(a)的参数与图1 相同, 图(b)的参数与图2 相同
Fig. 4. The interaction solution (49 ) with parameter satisfying Formula (48 ). The free parameters are chosen as {n = 0.4, a 1 = 1, a 2 = 1, a 3 = 2.2, k 1 = 1, k 2 = –0.22, ω 2 = 1, α = –400, β = 80}.
参数关系满足(48 )式的碰撞波解(49 )式的演化图. 自由参数为 {n = 0.4, a 1 = 1, a 2 = 1, a 3 = 2.2, k 1 = 1, k 2 = –0.22, ω 2 = 1, α = –400, β = 80}
Fig. 5. The interaction solution (49 ) with parameter satisfying Formula (48 ). The free parameters are selected as {n = 0.6, a 1 = 2, a 2 = 1, a 3 = 4, k 1 = 1, k 2 = –0.12, ω 2 = 0.1, α = –14, β = 6}.
参数关系满足(48 )式的碰撞波解(49 )式. 自由参数为{n = 0.6, a 1 = 2, a 2 = 1, a 3 = 4, k 1 = 1, k 2 = –0.12, ω 2 = 0.1, α = –14, β = 6}
Fig. 6. The density of u . The Fig. (a) is related to Fig. 4 and the Fig. (b) is corresponding to Fig. 5 .
u 的密度函数图. 图(a)对应图4 , 图(b)对应图5
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