激光与光电子学进展, 2019, 56 (5): 050601, 网络出版: 2019-07-31
非线性薛定谔方程的呼吸子解及其怪波极限 
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Breather Solutions and Their Rouge Wave Limits of NonlinearSchrödinger Equation
图 & 表
图 1. NLSE方程一呼吸子解。(a) a1=-0.5,b1=0.8;(b) a1=0.5,b1=1
Fig. 1. One-breather solution of NLSE. (a) a1=-0.5, b1=0.8; (b) a1=0.5, b1=1
图 2. Peregrine孤子解。(a) x1=0,t1=0;(b) x1=3,t1=3
Fig. 2. Peregrine soliton solution. (a) x1=0, t1=0; (b) x1=3, t1=3
图 3. 双呼吸子的碰撞。(a) b1=0.8;(b) b1→1;(c)双呼吸子碰撞的避免
Fig. 3. Collision of double breather. (a) b1=0.8; (b) b1→1; (c) avoid the collision of double breather
图 4. 呼吸子的碰撞与分离。(a)双AB碰撞;(b)双AB分离;(c) AB与KM孤子碰撞
Fig. 4. Collision and separation of breathers. (a) Double Akhmediev breather collision; (b) double Akhmediev breather separation; (c) collision between Akhmediev breather and Kuznetsov-Ma soliton
图 5. 二阶怪波的产生与分裂。(a)二阶怪波;(b)二维图;(c)分裂
Fig. 5. Generation and separation of second-order rouge waves. (a) Second-order rouge waves; (b) two-dimensional diagram; (c) separation
图 6. 双呼吸子碰撞。(a) κ1∶κ2=2κ∶κ; (b) κ1∶κ2=3κ∶2κ; (c) κ1∶κ2=4κ∶3κ
Fig. 6. Double breather collision. (a) κ1∶κ2=2κ∶κ; (b) κ1∶κ2=3κ∶2κ; (c) κ1∶κ2=4κ∶3κ
图 7. l1=-1.1705+1.4i,l2=-0.5+0.4i时双呼吸子的并行叠加。(a) x1=0,x2=0;(b)局部放大图;(c) x1=-2,x2=2
Fig. 7. Two breathers parallel superimposed with l1=-1.1705+1.4i and l2=-0.5+0.4i. (a) x1=0, x2=0; (b) partial enlargement; (c) x1=-2, x2=2
图 8. 三阶呼吸子的碰撞。(a)双重碰撞;(b)三重碰撞;(c)简并态
Fig. 8. Collisions of third-order breathers. (a) Double collision; (b) triple collision; (c) degeneration
图 9. 三阶怪波的产生与分裂。(a)三阶怪波;(b)等高图;(c)分裂
Fig. 9. Generation and separation of third-order rouge waves. (a) Third-order rouge waves; (b) contours; (c) separation
图 10. 三阶呼吸子的碰撞。(a) κ1∶κ2∶κ3=2∶3∶5且κ1=0.8;(b) κ1∶κ2∶κ3=2∶3∶5且κ1=0.6;(c) κ1∶κ2∶κ3=3∶2∶1且κ1=1.8
Fig. 10. Third-order breather collision. (a) κ1∶κ2∶κ3=2∶3∶5 and κ1=0.8; (b) κ1∶κ2∶κ3=2∶3∶5 and κ1=0.6; (c) κ1∶κ2∶κ3=3∶2∶1 and κ1=1.8
图 11. 三阶呼吸子的并行传输。(a) x1=0,x2=0,x3=0;(b)局部放大图;(c) x1=-4,x2=0,x3=4
Fig. 11. Third-order breather parallel transmission. (a) x1=0, x2=0, x3=0; (b) partial enlargement; (c) x1=-4, x2=0, x3=4
图 12. 四阶呼吸子的相互作用。(a)双重碰撞;(b)四重碰撞
Fig. 12. Fourth-order breather interaction. (a) Double collision; (b) fourfold collision
图 13. 呼吸子的简并。(a) AB简并与KM孤子简并叠加;(b) AB的简并
Fig. 13. Degenerate breather. (a) Superposition of Akhmediev breather and Kuznetsov-Ma soliton degenerate state; (b) degenerate Akhmediev breather
图 14. 四阶怪波的产生。(a)四阶怪波;(b)二维图;(c)等高图
Fig. 14. Generation of fourth-order rouge wave. (a) Fourth-order rouge waves; (b) two-dimensional diagram; (c) contour map
图 15. 四阶怪波的分裂。(a)一次分裂;(b)两次分裂
Fig. 15. Separation of fourth-order rouge wave. (a) Once separation; (b) twice separation
图 16. 四阶呼吸子相互作用的等高图。(a) κ1∶κ2∶κ3∶κ4=1∶3∶5∶7;(b) κ1∶κ2∶κ3∶κ4=2∶4∶6∶8
Fig. 16. Contour map of fourth-order breather interaction. (a) κ1∶κ2∶κ3∶κ4=1∶3∶5∶7; (b) κ1∶κ2∶κ3∶κ4=2∶4∶6∶8
杜志峰, 宋丽军, 王艳. 非线性薛定谔方程的呼吸子解及其怪波极限[J]. 激光与光电子学进展, 2019, 56(5): 050601. Zhifeng Du, Lijun Song, Yan Wang. Breather Solutions and Their Rouge Wave Limits of NonlinearSchrödinger Equation[J]. Laser & Optoelectronics Progress, 2019, 56(5): 050601.
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