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Bifurcations of traveling wave solutions for an integrable equation
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10.1063/1.3385777
/content/aip/journal/jmp/51/4/10.1063/1.3385777
http://aip.metastore.ingenta.com/content/aip/journal/jmp/51/4/10.1063/1.3385777
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The bifurcation of phase portraits of system (6) in the -plane. (1–1) , , (1–2) , , (1–3) , , (1–4) , , (1–5) , , and (1–6) , .

Image of FIG. 2.
FIG. 2.

The bifurcation of phase portraits of system (11) in the -plane. (2–1) . (2–2) , . (2–3) , . (2–4) , . (2–5) . (2–6) .

Image of FIG. 3.
FIG. 3.

The bifurcation of phase portraits of system (13) in the -plane. (3–1) , (3–2) , . (3–3) , . (3–4) , . (3–5) , . (3–6) , .

Image of FIG. 4.
FIG. 4.

The level curves defined by of system (6).

Image of FIG. 5.
FIG. 5.

The profiles of solitary waves and periodic waves of (1) with . (5–1) When , , uncountably infinite many solitary wave solutions of peak type of (1). (5–2) When , , uncountably infinite many solitary wave solutions of valley type of (1). (5–3) , , uncountably infinite many solitary wave solutions of peak type of (1). (5–4) , , a periodic wave solution.

Image of FIG. 6.
FIG. 6.

The level curves of defined by of system (6).

Image of FIG. 7.
FIG. 7.

The level curves of defined by of system (6).

Image of FIG. 8.
FIG. 8.

The profiles of periodic cusp waves and peakon wave of (1) with .

Image of FIG. 9.
FIG. 9.

The profiles of breaking loop solutions of two families of (1) with . Parameters: , , , . (9–1) . (9–2) . (9–3) . (9–4) . (9–5) .

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/content/aip/journal/jmp/51/4/10.1063/1.3385777
2010-04-27
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Bifurcations of traveling wave solutions for an integrable equation
http://aip.metastore.ingenta.com/content/aip/journal/jmp/51/4/10.1063/1.3385777
10.1063/1.3385777
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