By Bruce Stokes, Director of Global Economic Attitudes, Pew Research Center

Special to CNN

Japanese Prime Minister Shinzo Abe travels to Washington this week to meet with President Barack Obama. This will be their first meeting since Abe was chosen for the second time to be prime minister and Obama secured a second term at the end of last year. But how do ties stand between the two countries?

Both leaders are riding a wave of relative popularity at home, strengthening their hands in dealing with mutual international challenges. And, unlike the Japan bashing days of the 1980s, when fear and resentment poisoned popular sentiment, Americans and Japanese actually like each other now. But public opinion on specific issues in both countries is likely to shape what Abe and Obama can and cannot accomplish.

The Obama that Abe will be meeting is in a stronger position than he was during much of his first term, enjoying a 52 percent job approval rating, according to a recent Pew Research Center survey. Among Japanese, about two-thirds back the Abe cabinet, at least according to a late January Kyodo News survey.

Meanwhile, about six in ten Americans today trust Japan, according to a Pew Research poll (the only nation they trust more is the United Kingdom, which is trusted by three quarters of Americans). And Japanese return the goodwill: 72 percent have a favorable view of the United States, one of the top favorability ratings among the 21 nations Pew Research surveyed last year. Moreover, three quarters of Japanese have confidence in Obama (compared with 25 percent who had confidence in George W. Bush in 2008).

But despite their affection for Obama, the Japanese are also disappointed in him. In 2009, just over half of Japanese expected Obama to get international approval before using military force, but only 29 percent say he has. Similarly, 58 percent thought he would be evenhanded in his handling of the Israeli-Palestinian dispute, yet just 17 percent say he actually has been.

All this suggests that when the Abe-Obama discussion gets down to concrete issues, there will be agreement, but also some differences.

The Obama administration would like to see Japan join the Trans-Pacific Partnership, the trade deal Washington is negotiating with 10 other Asian-Pacific nations, which the White House hopes to complete by the end of this year. The economic benefits to the United States from the agreement would increase greatly if Japan is a member. And while TPP has little name recognition among average Americans, 60 percent do believe that increasing trade with Japan would be good for the United States. But Abe is wary because less than half of Japanese support joining TPP, according to a late 2012 Asahi Shimbun poll.

Japan’s growing tensions with China in the East China Sea and its implications for the U.S.-Japan military alliance may also be high on the agenda.

Americans have somewhat hawkish views on China, and when asked which country represents the greatest danger to the U.S., more Americans volunteered China than name any other nation, including Iran and North Korea, in a recent Pew Research survey.

And Americans and Japanese are both similarly skeptical of Iran acquiring nuclear weapons, with 94 percent of respondents in both countries saying they were opposed to Tehran doing so, according to a 2012 Pew Research survey.

But what should be done to prevent Iran acquiring nuclear weapons? Most Americans supports tougher sanctions, and Washington has leaned heavily on Tokyo to reduce oil imports from Iran (which it has), a topic Abe may hear more about in Washington. But those Japanese opposed to Tehran’s nuclear ambitions are less supportive of such economic penalties, and this difference in opinion may weigh on the Abe government’s willingness to ratchet up Iranian sanctions in the months ahead.

Japanese and Americans also differ on the use of military force to stop Iran acquiring nuclear weapons. Fully 63 percent of Americans who oppose Tehran’s nuclear ambitions would consider such action, while only 40 percent of Japanese agree.

Ultimately, the U.S.-Japan relationship has gone through numerous ups and downs in the last few decades. Americans’ fears that Japan Inc. will overwhelm them have subsided. Yet challenges remain: how to jointly deal with China, North Korea and Iran, and whether Tokyo will join with other Asian governments and Washington in creating a transpacific free trade area.

The Abe-Obama summit cannot be expected to resolve all these differences. But the Japanese and American people are more predisposed to resolve their differences than they have been for years. The summit could not be happening at a more opportune and critical time.