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PureMathematics
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,2022,12(3),434-440
PublishedOnlineMarch2022inHans.http://www.hanspub.org/journal/pm
https://doi.org/10.12677/pm.2022.123048
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OntheIntegrabilityofNonlinearMixed
GasEquations
YangjieJia
DepartmentofMathematics,NationalitiesCollegeofQinghaiNormalUniversity,XiningQinghai
Received:Feb.16
th
,2022;accepted:Mar.18
th
,2022;published:Mar.25
th
,2022
Abstract
Inthispaper,thetheoryofreducedperturbationmethodiswellinvestigated.The
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[J].
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,2022,12(3):434-440.
DOI:10.12677/pm.2022.123048
\
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solitarywavemodelof(1+1)Bose-Fermimixed superfluidgasisgiven,theanalytical
solutionofits nonlinearwaveequation isgiven,andtheinteractionbehaviorofsolitons
isdiscussed.AcoupledKdVequationisobtainedbycalculatingthetwo-dimensional
matterwavepulsesinBose-Fermimixturegas,includinglinearandnonlinear,and
byusingthereducedperturbationmethodundertheconstraintconditionsofunitary
system.Theintegrabilityoftheequationisfurtherstudiedanddiscussed.
Keywords
Bose-FermiGasMixture,SolitonSolution,ReductivePerturbationTechnique
Copyright
c
2022byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution International License (CCBY 4.0).
http://creativecommons.org/licenses/by/4.0/
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p
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p
{
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2
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2
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µ
p
A
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n
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(14)
DOI:10.12677/pm.2022.123048437
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c
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p
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2
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c
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1
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c
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1
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2
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c
b
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r
b
0
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A
2
r
b
0
+1
b
+
c
b
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c
b
1
√
r
b
0
+
r
b
1
+1
A
2
r
b
0
+2
r
b
1
+1
b
= 0
∂A
p
∂t
+
∂A
p
∂x
∂ϕ
p
∂x
+
∂A
p
∂y
∂ϕ
p
∂y
+
1
2
A
p
(
∂
2
ϕ
p
∂x
2
+
∂
2
ϕ
p
∂y
2
) = 0
−
1
2
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2
A
p
∂x
2
+
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2
A
p
∂y
2
)+(
−
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A
p
+
A
p
{
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p
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p
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2
+(
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2
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p
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p
0
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1
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2
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DOI:10.12677/pm.2022.123048438
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[14]
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[J].
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(
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),2007,43(4):41-45.
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,2020,1(2):
94-104.
DOI:10.12677/pm.2022.123048440
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